(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 41455, 1263] NotebookOptionsPosition[ 38671, 1160] NotebookOutlinePosition[ 39051, 1177] CellTagsIndexPosition[ 39008, 1174] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Very disorganized Henon stuff", "Subsubtitle", CellChangeTimes->{{3.4179769242630243`*^9, 3.417976928912321*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x_", ",", "y_"}], "}"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"a", "-", SuperscriptBox["x", "2"], "+", RowBox[{"b", " ", "y"}]}], ",", "x"}], "}"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "]"}], "\[Equal]", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4179753510122213`*^9, 3.417975378508305*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"y", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}], ",", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"y", "\[Rule]", RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], "+", FractionBox["b", "2"], "+", RowBox[{ FractionBox["1", "2"], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}]}]}], ",", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.417975380737529*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "x"}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.417975458073389*^9, 3.417975465704748*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"a", "+", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], ",", "x"}], "}"}]], "Output", CellChangeTimes->{3.417975467713437*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"First", "[", "%", "]"}], "\[Equal]", "x"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.4179754728915043`*^9, 3.417975479691187*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}], "}"}]}], "}"}]], "Output",\ CellChangeTimes->{3.417975480246574*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{ RowBox[{"First", "[", "%%", "]"}], "-", "x"}], "]"}]], "Input", CellChangeTimes->{{3.417975490815913*^9, 3.4179754981237993`*^9}}], Cell[BoxData[ RowBox[{"a", "-", "x", "+", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}]], "Output", CellChangeTimes->{3.417975498642036*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"henon", "[", RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "]"}], "]"}], "\[Equal]", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], ",", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4179753510122213`*^9, 3.417975378508305*^9}, { 3.417975538757079*^9, 3.41797554225735*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"y", "\[Rule]", FractionBox[ RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "+", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]], "-", RowBox[{"b", " ", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b"}], ")"}]}]]}], ",", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "+", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"y", "\[Rule]", FractionBox[ RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "-", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]], "+", RowBox[{"b", " ", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b"}], ")"}]}]]}], ",", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "-", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"y", "\[Rule]", FractionBox[ RowBox[{"1", "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"], "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "-", RowBox[{"b", " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b"}], ")"}]}]]}], ",", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"y", "\[Rule]", FractionBox[ RowBox[{ FractionBox["1", "2"], "-", "b", "+", FractionBox[ SuperscriptBox["b", "2"], "2"], "-", RowBox[{ FractionBox["1", "2"], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], "+", RowBox[{ FractionBox["1", "2"], " ", "b", " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}]}], RowBox[{ RowBox[{"-", "1"}], "+", "b"}]]}], ",", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.417975573407462*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{ RowBox[{"henon", "[", RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4179753510122213`*^9, 3.417975378508305*^9}, { 3.417975538757079*^9, 3.41797554225735*^9}, {3.417975599953561*^9, 3.4179756080090837`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"a", "-", SuperscriptBox["a", "2"], "-", "x", "+", RowBox[{"b", " ", "x"}], "+", RowBox[{"2", " ", "a", " ", SuperscriptBox["x", "2"]}], "-", SuperscriptBox["x", "4"], "-", RowBox[{"2", " ", "a", " ", "b", " ", "y"}], "+", RowBox[{"2", " ", "b", " ", SuperscriptBox["x", "2"], " ", "y"}], "-", RowBox[{ SuperscriptBox["b", "2"], " ", SuperscriptBox["y", "2"]}]}], ",", RowBox[{"a", "-", SuperscriptBox["x", "2"], "-", "y", "+", RowBox[{"b", " ", "y"}]}]}], "}"}]], "Output", CellChangeTimes->{3.417975616333123*^9, 3.4179765403738527`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"Last", "[", "%", "]"}], "\[Equal]", "0"}], ",", "y"}], "]"}]], "Input", CellChangeTimes->{{3.417975641049087*^9, 3.417975647439468*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"y", "\[Rule]", FractionBox[ RowBox[{ RowBox[{"-", "a"}], "+", SuperscriptBox["x", "2"]}], RowBox[{ RowBox[{"-", "1"}], "+", "b"}]]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.41797564820685*^9, 3.417976543235937*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{ RowBox[{"First", "[", "%%", "]"}], "/.", RowBox[{"y", "\[Rule]", FractionBox[ RowBox[{ RowBox[{"-", "a"}], "+", SuperscriptBox["x", "2"]}], RowBox[{ RowBox[{"-", "1"}], "+", "b"}]]}]}], "]"}]], "Input", CellChangeTimes->{{3.417975689671496*^9, 3.417975709380705*^9}}], Cell[BoxData[ RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "a", "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "+", "x", "-", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"a", "-", "x", "+", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], ")"}]}], SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b"}], ")"}], "2"]]}]], "Output", CellChangeTimes->{3.417975709958606*^9, 3.417976545606884*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", "a", "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "+", "x", "-", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], "\[Equal]", "0"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.417978837975543*^9, 3.417978842759131*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "-", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "+", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}], ")"}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.417978843654645*^9}] }, Open ]], Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", "a", "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "+", "x", "-", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], "\[Equal]", "0"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.417978837975543*^9, 3.417978842759131*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{ RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "x"}], "}"}], "]"}], "-", RowBox[{"{", RowBox[{"x", ",", "x"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4179753510122213`*^9, 3.417975378508305*^9}, { 3.417975538757079*^9, 3.41797554225735*^9}, {3.417975599953561*^9, 3.4179756080090837`*^9}, {3.4179758287923813`*^9, 3.417975836587862*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"a", "-", "x", "+", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], ",", "0"}], "}"}]], "Output", CellChangeTimes->{3.417975837906398*^9, 3.417976550514619*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{"%%", "/.", RowBox[{"a", "\[Rule]", RowBox[{ RowBox[{"3", "/", "4"}], SuperscriptBox[ RowBox[{"(", RowBox[{"b", "-", "1"}], ")"}], "2"]}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4179760540343246`*^9, 3.417976066581311*^9}, 3.417976134796949*^9, {3.4179765532682962`*^9, 3.417976555239743*^9}}], Cell[BoxData[ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"3", " ", "b"}], "-", RowBox[{"2", " ", "x"}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "+", RowBox[{"2", " ", "x"}]}], ")"}], "3"]}], RowBox[{"16", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b"}], ")"}], "2"]}]]], "Output", CellChangeTimes->{3.417976067658184*^9, 3.417976135858235*^9, 3.417976557435522*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{"%", "\[Equal]", "0"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.4179760721293707`*^9, 3.417976074563264*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x", "\[Rule]", FractionBox[ RowBox[{"1", "-", "b"}], "2"]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", FractionBox[ RowBox[{"1", "-", "b"}], "2"]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", FractionBox[ RowBox[{"1", "-", "b"}], "2"]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["3", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b"}], ")"}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.417976075113145*^9, 3.4179761453103113`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", "a", "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "+", "x", "-", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], "\[Equal]", "0"}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.417975873531913*^9, 3.4179758777588778`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "-", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "+", SqrtBox[ RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"4", " ", "a"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}]]}], ")"}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.417975878227777*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Collect", "[", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", "a", "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "+", "x", "-", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.417975888971196*^9, 3.417975893040304*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"-", "1"}], "+", "a", "+", RowBox[{"2", " ", "b"}], "-", SuperscriptBox["b", "2"], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "b"}], ")"}], " ", "x"}], "-", SuperscriptBox["x", "2"]}]], "Output", CellChangeTimes->{3.417975896942359*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{ RowBox[{"-", "3"}], "+", RowBox[{"6", " ", "b"}], "-", RowBox[{"3", " ", SuperscriptBox["b", "2"]}]}], "]"}]], "Input", CellChangeTimes->{{3.4179759555491962`*^9, 3.41797596024655*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"-", "3"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b"}], ")"}], "2"]}]], "Output", CellChangeTimes->{3.417975960794945*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Transpose", "[", RowBox[{ RowBox[{ RowBox[{"D", "[", RowBox[{ RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "]"}], ",", "#"}], "]"}], "&"}], "/@", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.417918957816882*^9, 3.4179189775817947`*^9}, { 3.417976783595872*^9, 3.417976784600252*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "x"}], ",", "b"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.417918978540145*^9, 3.417976670194971*^9, 3.41797672948392*^9, 3.417976785139732*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eigenvalues", "[", "%", "]"}]], "Input", CellChangeTimes->{{3.417918992115902*^9, 3.4179189976325817`*^9}, { 3.417976786717083*^9, 3.417976787540289*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "x"}], "-", SqrtBox[ RowBox[{"b", "+", SuperscriptBox["x", "2"]}]]}], ",", RowBox[{ RowBox[{"-", "x"}], "+", SqrtBox[ RowBox[{"b", "+", SuperscriptBox["x", "2"]}]]}]}], "}"}]], "Output", CellChangeTimes->{3.417918998272421*^9, 3.417976671949099*^9, 3.417976731097361*^9, 3.417976787996664*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "x"}], "}"}], "]"}], "\[Equal]", RowBox[{"{", RowBox[{"x", ",", "x"}], "}"}]}], ",", "x"}], "]"}]], "Input", CellChangeTimes->{{3.4179766506938057`*^9, 3.4179766627131042`*^9}, { 3.417976733108471*^9, 3.417976733370084*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "b", "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}], ")"}]}]}], "}"}]}], "}"}]], "Output",\ CellChangeTimes->{{3.417976723570354*^9, 3.4179767339070177`*^9}, 3.4179767898654413`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{"%%", "/.", "%"}], "]"}]], "Input", CellChangeTimes->{{3.4179767387106133`*^9, 3.417976744509338*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "-", RowBox[{ SqrtBox["2"], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"2", " ", "a"}], "+", SuperscriptBox["b", "2"], "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "-", RowBox[{"b", " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}]}]]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "+", RowBox[{ SqrtBox["2"], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"2", " ", "a"}], "+", SuperscriptBox["b", "2"], "+", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "-", RowBox[{"b", " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}]}]]}]}], ")"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "-", RowBox[{ SqrtBox["2"], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"2", " ", "a"}], "+", SuperscriptBox["b", "2"], "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "+", RowBox[{"b", " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}]}]]}]}], ")"}]}], ",", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"1", "-", "b", "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "+", RowBox[{ SqrtBox["2"], " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"2", " ", "a"}], "+", SuperscriptBox["b", "2"], "-", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]], "+", RowBox[{"b", " ", SqrtBox[ RowBox[{"1", "+", RowBox[{"4", " ", "a"}], "-", RowBox[{"2", " ", "b"}], "+", SuperscriptBox["b", "2"]}]]}]}]]}]}], ")"}]}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.417976747248829*^9, 3.417976792842621*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{"%", "/.", RowBox[{"b", "\[Rule]", ".4"}]}], "]"}], ",", RowBox[{"{", RowBox[{"a", ",", RowBox[{"-", ".1"}], ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.417919765573018*^9, 3.4179197806068277`*^9}, { 3.417919826086895*^9, 3.417919832550829*^9}, {3.417919865947134*^9, 3.417919873613598*^9}, {3.4179203823019753`*^9, 3.417920385154808*^9}, { 3.417976757468726*^9, 3.417976812464356*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwV03k41GsbB3BJUYNCdaYjJ5IoTnktEdUzWk5kLZUtCjmNEo5sWUqyb4lo 3ldFGFnCGGNCuBlLlrHMDDND2cq+ZKvXGufXH/f1XJ+/vvf3vq7nspuDnJOA gIAgNpG/Xni/HQcVcy7QHRkivs/nJbwXNCk9U6YK3eqwbROTCvQptfThMFPg d/m+UHd9CHTuntgIc1fgkxbVd6j+ADqs+CrLxgDfWVQ44BQB6Dl9Dq3TecAn GA3b+v8G9ESGsXt5M/D3WZ7b5hEO9MAsbanwMeCtDmYm6BYC/XbUAfpVYeD1 Sa+rZKcB/ZKrmNWBQ8BjPDSltfYBXUHzy+sKR+DFm8UvPn4J9B17W/Uig4H3 4Mz15uk5KFn6+X7oWhrwHC8bqK/sghJmfezh2T7g6RjURNpaQInnVa0SBUvg zkmzN6t2QondiQMW8z7AHTAMUdCfhxJ9GdEVSAZu+8qi+ItoKJEe+kKw4gCX QiuyzuADrdYzpiXOBLjejc1WIYNAy7f0cbVxAa7zgdQ2BTugvTjpIKEUDVyb xt8UHUKBdldI6xqjEbh6I8eXSESgSSYODi6eBa6EpIGo5GkoXkmh4VA6cIXc q/qSqFD8JSNMI0IAupZwxyzkdKGYWnwkHF8BXf3jbp9ajkHxZfZ9FZ3j0EXF mTyW3wHURAkh78Aj0GV36dEbpXSg+uO5qfUR0HXlYVZyshJQHWWzm8RGoesi 875LSxhQ1VWNpV9nQpdWw3bZ8rtQxDFNqq6WgS4pvESYQSYUScUp4jbvhM62 OMMJ+j6grCYtaxi6QmfDLcPPl5OB8vVVi21iK3RWmTrZTIgDpTjfjXIwCjoL HGY5VTFAMWeWXv1rM3Q+9ShtsEiGQqU9iUhiCjqvfJaf69+Ad4d38okypcCZ eEuee5AJeWvGNW6evsAZ4p9eOSsAee1Rud4tJ4DTL1naRWiDPG+hgFDfcuBw MsvMtQshl7Ekm86pAE7lia0OK+cg53o/sTeyGjgJW5XXvZYgKz5/+fKPRuDo uVE2xocgy3Hii7VRBHBOvgnW0w+DLC3FFvsMA+Bodbc6h1KB3PvmlbtZM3CO 2oY6UUhAPpKkF5vHBI50od/aJwpk1AVENtp3AHvRNbD3fB2kLRn+fqqVD2zq zFkr23OQxiS2uJDdgV0wXKwd4wlpaWEBKYEiwM4dSE4yw6xf07esog3s9K+x LEsapKr9c8F5txqwE2XkduVshZeeRtbX4mjA9rxG/Cs+BpKXBIP+87gU2Ccy w3KbCRC+3vuirT0YWG37AvOo2RBOuE+qEh4AVnOeY9vI3xAWvO2/+YTTwPp4 yjVEmQmhWzRToimrwKq+080aFYVgXGyqfoInsKgTTuJRe8BX1d84JJcJLJLP vYTrfoBv6+mZJhOA5US218tUQuEp6SqO+GlgCdtc27JmhyKMLfBpjUHAEqo0 vZPFRBEbokJ9vpLAEpTb5UnCoygHr14rnjZ0rE0v+tlmodjDBnFmSSHQMf/y c2TOO/TMxtd3/zYx6OgzFstI90DJ4/t7REMzoYM+am9vvwu9EdQyWQBn6HB5 bi++vILycQmmz/Dl0F6mPX0jNBPRXG0zFP+QhDZGgYh8/ztUNmcQPjVjBq0/ xiuzZ1wQTOpGS82mQetRgfILKtWIAQx/FvZfmCHRhmoKA6jev6cwTbkAWibn bz0VN0ON973mU7k50GJuMqJeRUEt2icnzOWcobnd7vyFxVnUph02pyWkBs0X DUT+JyeCOpIcdFgu1dDU4XWs++5NxPqxh2eveBGanNroT+ZIiOMRsxr5Jx8a l8Y8a24EoU4uaQUnpA+NpJW7trcGENfy7yCFQ5XQeDwjO/1qEOJx/qzffMYL Pn7SuS72LRt1a0QN6R7dAR+j9qf6OFminuKcaJxTAXw8bvk988MY+rzXTlTz 3jFomHy/e2qnGer1FTWSv7cADWRy5Ce8Ger7HiCVU/4BGq7zcMw+JTSgXN1T N1kMDdKU+46JpWhg6qDbY1kc1PNG2rY/E0GDOUJfUy9tgXqSoM2OWwT0xUr1 3ITzLNTbpY2Ls/HoK/7knU3ZvVB/IDvFX80XfW1ODDjf/gHqpnIVLh1MQ0MP bt+bXNCFujL/wfM6pWhYa5+83clKqHvSvKBzJwINj0nX/3RVhTrzK62VqrNo 5O2aCrGeDHWyDwqMJIho1EYxaNMWHNTO+7kIDBHQ2PZ26qqeFNQ20Cos/EvR WJNlTk2GDNSS3jyYypxF4/4qsbRpPNS6DlqHr3WgCd1BTU/b3VB75ltM5+0I NLEsWZHURIPavcKpA/6yaDLnqerQH+eAsSBwcNSWiKaIU8R1EhcYzb3BeYvu aFr6edz5VStgZNlHOI6aoenmsoQZ64fAePLouGasLPoWATa3+snAsCM52UZH oBmdnRLCRpXAOCU4vD+OgGZW9KK8+vnA2PtIyIBCxGwZIs0ewuzHUUhxx+wW WFM/g9k7XagmHvOrf8TebcXsiphVs5iXLci+mpht/Z8EYl4tOti1MwGz7kKM SCOa+SkLGnpGwMAvjWxTL8WsVdqjYYn5e4mRbzVmE2qQoiPm2ZCEJSz/ZwCZ KeaHeUz+8FtZzPwYx+4czLybgQwzNLMeb5XogeXjSz5VT2L7rb81P+Ekibko T4sngrnKqN9SBnO+X9EaH/MUQfm0Bmby3sJFrO+G/qHa7b/ynluwsywx35Al /nTFHK/o6IjdZ8P7d/HZX/nR/1+0HsCcKWbNxfrgnyQrLWJ9Nj4ICzS9xvzI qeHVTcxsgayKX/v5a94OFMA8tmJUSMPsswWXjPXb2FiYT6/G7NFJnSD+CwYu uBw= "]]}, {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData[" 1:eJwV0Xs01PkbB/BhZvAzKcxZq3TRRSoqWnKt58PWrt2UKJfpoi2by6/SZfDT z2UtZVCh/MhurGmKTHaWDINJPqOWtlxzC78SQi5j50bGuMx+/fE5z3md55zn /Tzn43XxzPqzJBJJk3iXlyqu0KXhatl5kOrSG3X6J3CF5qFK1yorkCJuf5HJ USwQ7+IMJ3qANPaE8IxjBxZ0Gd1KOhIK0oK/lQ2+cizAqkgL05sgfZnnQes0 wQJu35mmySKQfmyt73g3jwUZzw9eEr4G6QJJdMxfggUxBfZ01ijI6Gpv3stG LAhK2SDw1gbZVvch5ttQLPAM1WNs2AyyPeDwy9pRLDCzHfytOgBkp6d3GvzJ wYIVK5tckuNBxtR+H7+PgsuVCxVDPmyQJZwdrxnwweWNdbe2SvtAxvHZ/FNm Jy4P87YrN/MDWW/miE33CC73d9jgK/8PyD6VOxgwHHG525plKpwFsqmEo8Nj 6bjcZGgQMdpBrufaktb/GZe9CLvZkHoI5E7N3vfui3GZYcbAwMzXIE/r6Xm3 5RLmq+6V0YAD8l9/GvdSj2D+4INEmyQSyB+qPSVmyzG/lL+NZVwN8qr09rIW BuZ7tTEtHXeDfMB857kEJS7NMKBExGwDhYUp825UDn5CTzWnkfVBUXy7MGk+ HpfMZc7aHAgFRcUho7jvY3HJx9yGkxlNoKiZvx7O6sMlfN7Fkk0poGi2KqDW 6OKSI42V3t+QQTGxuCKZIcLFW4wywEAMU2aBzB/ytfHvW/W7g9dUwlR6x1cp ijxcNH+w9mJYJExldXZar4/DRS0pjyMaHGAqp1X4f7QKF0VQoq9HCmGqsLRU HcnHj58rTTnt1TAl2vquvckVc098CH6fLIKpyZmH37auxgXpvFmv6b9gen/a 3f7e85itPLBqT1M3TH8qOnguXYDZjcEN5/MvwbQ4yNhzNwOz2YnR92J0YFq2 rowcMILZbrV9s5b2MK1iXU26a4fzdl3+NuSLXfBZz3q2qpaNc8Lcj/mklsFn a2VgXm0TzlJqxln/XAmfrzKD4trCMGvx/d3mlniY0diRUL2XDax7HMsA40lQ 6hX72ZXaw31Nu0MKHAJK6fGRx2Q34NHueNw2FsJsW8XOZ9AFZaEnH5ivNQTV /eKEt+sKoUr2HUssOQxzvnxHh9FrgCecbtClbJina1krctjwHD+PekP873xV j0GuUSvURfUWsy3+gAWft6623wzCX8xweV4XFxZUwthBHAoN9s7jR9aHwGLq Pn2PbCtotk+U2VF2gXqLdNHqHQ9aM884vjkvAvVT9R5j1SV4M2309rT594hk ym4d0rOC9is355K3dyNS4JQqw+5f0NGVraJR3BCpQPy69rgYuvwC48w2P0Ok 8VszK6Vp8LZ9ex3ZNRxpWJy6dviRHHpsUoacdqxAGoGsjF86dKGXz71BO/sH 0sg/mhikJ4R3K/2X2V7YiTT6XgUNqunwPnKZ+8YLCqRpRI+rSCND31Q0nSt8 ijQPT+MfUnWg30LU++cEH2kmSkr65+uhX7zp4s+mNKQpCi3NrqmEAS7lY54n FWnOjPtnXdaBQYbVvvEQKSJv67G3Fm+Cj8bO/9YofI/Ip51JuS+z4ePrjOj9 LU8ROWOvkeWXkzB0NejChMIJkV9k8j8gVxi2W73R3/kZIs94ZF1X7oDhUZO6 hVArRNk87o22i2Hk0bxlcF0+ojA6heFeKvh03DxOg0pDlKQXXhFxMhjVbSmd c6EjimA365EAwegrP27tgzWIMjLm6l89DGNRlrfKJo0Rlf4G9btdgnGnAduw k18g6tej9Y22fTA+a1id+aoMUa/cNqfFF8AEN81qaO0+RM3N2UG2bgZxsDh4 MbsLURvqA5p4HTBp8r/U/XMMRP0cIolin4PJ11V3JMdikda6hv6hjTnwdxI+ /uOHfKTlvufX+rumIHHUN9B2f4a0wt2fret2BonKJSX8QzfSuu+vNxuuQ9jv mknbEOGAA6Ib9oQvxtTWSQgHJydSWgjnXtb7XYswk7psw1J/1jc/0pYwa56q tQokc082derfIfxkjMuMBMmCKbZxcUdaHOqLagkibFfZa+NHmKZxOPwrwodK 48wDCOvvHfSvIRyd36j3X8KrhBon2IS7bwb0cAnvLLEkV4NkMZ2RcYXI5zBy bEg8wo+OOJw1JOzfwxO9Jlzj/sFvDeEfvzQbyiIsRhZ7bQiH3jHw3Q8Stdvm F7pLeQmsjrHVhE+ZBi+EEk6qc6nvJxyxarl0KT9Vk6dzivBDvWNdxD2c7JhY ATFP/VSb9Oo3wrnC4Y2ehNtIBdVL+3GU3ymaCI+q3IvLCBfa8rYsJ6xWyDki wjzmcpHhP9LkoRs= "]]}, {Hue[0.1421359549995791, 0.6, 0.6], LineBox[CompressedData[" 1:eJwV0Hs4FPgaB3AypXUpl6XZrFsYbYRT4yDllza6oN14qpFlN6KRGinkMM7W nphYymV1OkprlTQkl2HSYF+K1jUVuYwxMxiXGAaTzMXl/PaP3/M+n+d9nvf7 vj/fyGDzUBUVlXX4Rfxd4bmGJtTNX4ABZv0fbwLJ8HzdsZoDLxyAq9rkGKLZ A2zxroKx5O+AG0ZvSaw7D+xew/SbfjTgMi+5j2x/DmxQxNmYpQFX0Bl70zgL 2Ex+cOdMCQxuWs2JqGsGdvZLn0ucNhh0CbU2uGcK7MTHzvqMSRj8yafY920X sM+lbmOfUIfBG0nWnV14/nGatv82Egw+/i0/ZSAa2FaOIw/qQmBwrLBjII0A 7M1fdbqn/AI8NatH+qEeUC1beS46mQ88U4bP2Z9jobqjOf2bOT7wTlzu36js hOroE07VVhTg1YRtN1BkQHWQy7ZTC1eB11VULKJRoPqwsZYC7gBvPDzo7o+v oNpINLLfvxuG9DJfbzq4FapeRae13zoGQ2HuyC3hBVTpZQ8PL30LQ2t0wn5m BrAU96o0UQHw9YlXLD60AGvkYTL5pgrwSXE9bsdLgVXJ2sEg1gHf+/YyL+R/ wPJ9f8V2zz+Bf4dCcPxhCSqzdQmxiTtAYD7cEe87BRX6t6w11XRAqJP7vVxI g3JljpzsRQMh0ebC9XQ7KB/Naw/M7gShaYUkIK8MylmlkeWWqSC0y7fs374T yv06ak54qoHQW70wKv0QlG03zEa6YhAm2QeTBGR4+o1OP9W4BoTzsgqotYeS ZZ/GyOg4EMpMBW1sEpR0pRbHtruAcPWArv2hcCiJJdCT4jgwrHG1pegfWVD8 UmZW0F0Hw9uK6aGbHID5g4A6lNIAw76ubhuI4/A4o1Tuu9gCw88ijnQfKYB8 mdfWfZ39MBJ4dGWRvxEYq0P/fdP1C4zm2sZOFjojxr0C2xDiDIj6ZM6p7zrQ H+ucjkkhHMYk4pEl1mdUqpn1XSaRAxO6015RFkpURQt8aG2iB5MWUkY+tQC9 mD/CEEu+h49GtboNSIRg2vVX/bl8mDK3qlZkGqGX8DLhHf7/6c2uE2d3e6Dm BG5Zvs0zmJYWkzsPvkYtV2IWfu9lgng8wTjXPgy1O++d8jMPh5kmTqhU7Ize OCfPOxF2wWyFV3tM/CX0Nid4z7sLDSDJiXHbY/Ilerdo2HfG+ijM7Y7QKghV oO7LacqUnf0w99DpQKPLA9TTe1ehSTgM8xpqGg6SVtRLCbtmRaqH+avtTu2M z6ive2ez2oEYmB/ZaDpjcg4NkFNFrnabYeHbbg2JWyrispi/aoY+g4Wn8T6u 54MQ76sgLceL9iDVkvrn9A2ioTgtb4uLUpCeD2+Nuy1E/E90fSanFqRvcv/z ltGNhDYN3KZpFnyyUTNUeLxFQrFl5HUzTfh0a/0Z4cYeNMwkjP5+fD18mt16 v7+xD434OxycCp+DRc/G5tnUDWiUuPe86pMhWCwU5s02LaPRtmy6R1ctLK78 6em+uoZE/zp3cVrqCp/9vlDdUf4EjTl9bRG0tx4+PyvZorLqhMYmjZpXaA6w pObXkOHtjcaLlm2pzYWwFOQUssinookA62uq6zVhqdJTYXCShCY1uiqV7vog U5P+5XmfiyZbKczGh8YgC6i/l97ShD4m2KZXzRBB9nTO3S2YjKZchx2jAw1A TiBtIdoUoCm5Xl1OaxXIKWsiTqIemmbedhCZHAR5UYKBT3sAElPF1NW7vSBX DgXOM/ajGaPfbnko/UFxZKWxNLQNzbS9yJKc/jcocpTl9OtRaPYmBJwVFIJi 4nW8pdEEkuzR0VX3rgfl7p935CpOIonCPTVG0A/KG7NR1xaTsCk3jN6LsGUW d4K52JGJjc0SUCapfmDS/u7nRWk/3YBt4NLy0zi2/FRhnCP2XtWPFQokUVZY ftDJwk7J5GxYQJIVMyC7e4My2bIsk7GM7VTDJVOw7c6cfhWMfazymnUItrO+ eZ4vNr2wQzse2yv2ia0Quz8tZICJfXnfXQ4PSVYz/LMv4/xkaFfP7sEu8nMJ 1cNupRfXdGD/6S2gGGN323nRI7DF+23cyNjjmUkCJpKsHSa90sB5DO1TfMOj 2D+aUVdo2Fu+oDmUY8du3TSH8xlmHOXHNuxH2qd78T0MsomOsyV2rbpK6wPs fV13OsOx36s8rsP7MQ5dN1KlYk8qvMuqsI/vut9Dwl6TLhQ0YJ8Wfe3x6P/J GMB0 "]]}, {Hue[0.37820393249936934`, 0.6, 0.6], LineBox[CompressedData[" 1:eJwV1Xs0FNoXB3ChK89EtzuRm0dSqKgRethGyDulMlQoFb2oSG64ZAnJK3po KSYaNSFiTJQ6iHvJc8g0lPcwb6PUz2Oi37l/nLXX54+9v/usddY6B0JP6J2S kZGRxSfuv4peKSmj2q/nQSIcKnJRm0WvZD2q7WrMQBL70d7uoQxiiLYWjCfu A4nC08fXErchBmtVWrJXCEzW1G5xCiQjBpqPNNFNhcmoO0me/AeIQRs80S4u hknHs/f0nI4iRnaD+8XXH2Dyjz25pC2+iBFTZKWZxAOxKPZEzDEVxAhK0Wcc UgBxk45Z1HQGYuwPUfXRXw9iyqVzXtE2iGFoMZpXGwjiY1ctTQK/Icby1e2k m/EgtkkpZirMo6rZhVecwxQQ6ykcJQ7Hoqq2prSNU4Mg4uecNgvyQFXhhyyr DMkguiG9r+jihqr8rPW9v10FUciPW80ZOajKSUdlHt0DEfk2N0RNhKq0OaO2 Pj0g2pQgKyWEIfr78NTWdA8QDnggqf4XRNfIHhmZ2QNCj7m+g2HnUeV8Ll0Z CkC428S4/iEZVY4WJhKTZUBoQms80PsOVVZUGicRakGoeP0KeYiAKg90h5nu 2A6CZudyQV4kqsheIR8RYwwCTzB0MJ1GFVEEVn5TMgjsNOdOhlqiikDdZy2q XBAQNSNyI4JQxTYzd+28JyAgpJ2SXWuKXvbsu1tXpwP8MXf9WNI/6KVmupGy nDrwY9el7nk2iMqld+eIriHADzNq7U0aReVjj1qPZbcDP8hxIYHvj8orS0PL 16UAfx/r1cOvTajcq636kKMc8PVNnDecm0NlG1ZlwwoR8Fq3TzcKU1DJRnV2 sE418EyVEpbNbETFP93rQ8MjgWfg+MZVqoKKO1OeR7RaA08r08+5Qw4VR8hH 34h8DTxFV8NqOx563jCrW9BTC1yuT8khbyKiHR0KHrhZB1xq1aUvWuqoKLN0 7sCPZuAanyXPTOmjokDBqK9bMnANFLLmlotQkaVR6/FCZ+Bql7Z+zlqLqAOP H130/ABc1ZWsMnNPRDW+S0orboOJKZfy1fGqqLAx+mbz8S6YqCa9T+eoIcqs q9budjZMuHefM2c+QZS24Nbz1IswsTcxX5e+AVEoidG5MctggkTSR9fMEcWp fnDO1AomiM0j51gdKH/rpb1nft8KE2v0GjSIw+hhuJvv4XQ6jAvFn6gHZ9G9 Wdk48+vVMJ6Rp0/uuYaSFgfud3TGA2fcfmVJUAVKsg3LeacwDJyhlu51ivdR Yrzig1JbG+D0H9ycXDKAbiy1yL1VLgVOZ0Thm9R0FK+clu+UFQ6cmq8FDpkL KNIsyj3heRtwMmpc2X36iNDR3y+m2gLHxs958zwbknILTAMJYhgrKn2QwPwG j2UtPabRGRgtHi+5ndkMpcpZ+24TXsNIvXkaXbQW6CHHCo3+1IDhmaLg40kF UPPVOUkk8YRhT4swnRVrAAl33tKcosCQz6+OPzRGoQE1RDHxex50NJyvEf4G TVH9ZRSTFzDg8da/r34OmsOufMtn0eALOS42U9USWq12Cbz0zsDnhOFrWrZh 0GGV+NVSfiv0lzdKSP4x0HX3xA7m+Trok3wXtXwcAeaPVZ+OG7lAn5NPz9Xp X9BzOVV6cxMb2HkRu3Oev4GPrJx5ZXknYCtKeol+C8Ain44zXP8WPl3+/G90 Fh8+9WxqkrO7AixuOll20Rz6iCmcnZuXA+u8yCSizxX6K2m3lE+9gF6JjdPH 00HwZbWfisWFLdAbZxwru7MVBiJV3AwuTEMv4fnLYV0fGPwerUl7jXNLv5+e EkzDsEldf6OwEj7u2/bZ/98qGBatC72uqww94oD1qXZDMEKTH8vfvxR6bo// JbcoD6M+ZvaCM1PQY+t7/++f/TBG2HV2ybMB6Ba+T/PebQdjH7KjHTrfQDfF eO+a3BLg/BV0QTi9E7p9lhjoGlfAuOUaA79db6FbbWTSxjocxnnaTQshZsBs C7slNNKCiac/TYObqMBMsg5Y+8oXuEeM4pYsVQams7J3SMYs8JQ6K6QkTWCq 2Sn1umkAr4VMqy/Uga6ulnH5I2bAjzJNo4sJ0PUgPHKZeiIIdo5YhB/7Hbr8 71lvl1kPgjmN2rstdOja8M+MC/8yCGkZZpw/7aFzsiy5ljgLomBR8GIOCzoT pR3/E9eBWPtOuoPUBzo3uli+eHYHxB9qsiS+f0NHl5XDxdlkmExGR04OUaHj cqrBi6xgkOxQX6Hg9hY6dD4syY5oA8k8KeXKEBvaG4tdvKjV2OQE7W4ONqX9 TE4AdmhMfZME+57nzXjcP//okmrJb9jXD3N37cKe86ZGWmB7n9RyqAWJ9OW6 XvUsbLk4v4KLIFnQRUSSG7S/P1IXsNoe27K6n0jG3m9P78f9Cx4VcUaB2I4t mpnl2NHUNtVr2ObMyYE6bHZqYB8NW4GzZkYdJIuZPtmXcX4DXcmbMIz91Mv6 lAY2LcPV+CT2O7chsg52/kpnM7zvosjWxIaInfJn4Go2SH45rX+vhPMaArap BWRi++sGL4RgH6o+sLIEO0JLbQrnN7juzq/9gv1E1ZeF79Ow3YnMx//0rzcK Mi152CbtjRessLtlimrxfg16XtbjKti8ebcyOvYqdo3nf/N+TX8rqMNW8bMr +/l/yzwzjg== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotRange->{{-0.1, 1}, {-1.7205456648410768`, 2.8294323910595347`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.417976814883095*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor", "[", RowBox[{ RowBox[{"henon", "[", RowBox[{"henon", "[", RowBox[{"{", RowBox[{"x", ",", "x"}], "}"}], "]"}], "]"}], "-", RowBox[{"{", RowBox[{"x", ",", "x"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4179753510122213`*^9, 3.417975378508305*^9}, { 3.417975538757079*^9, 3.41797554225735*^9}, {3.417975599953561*^9, 3.4179756080090837`*^9}, {3.417976982244684*^9, 3.41797698464703*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"a", "-", "x", "+", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], ")"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "a", "+", "x", "+", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}], ")"}]}], ",", RowBox[{"a", "-", "x", "+", RowBox[{"b", " ", "x"}], "-", SuperscriptBox["x", "2"]}]}], "}"}]], "Output", CellChangeTimes->{3.417976985188072*^9}] }, Open ]] }, Open ]] }, WindowSize->{971, 646}, WindowMargins->{{14, Automatic}, {Automatic, 0}}, ShowSelection->True, Magnification->1., FrontEndVersion->"6.0 for Mac OS X PowerPC (32-bit) (April 20, 2007)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 120, 1, 26, "Subsubtitle"], Cell[713, 26, 268, 9, 33, "Input"], Cell[CellGroupData[{ Cell[1006, 39, 367, 11, 27, "Input"], Cell[1376, 52, 1610, 53, 79, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3023, 110, 171, 4, 27, "Input"], Cell[3197, 116, 200, 6, 33, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3434, 127, 217, 6, 27, "Input"], Cell[3654, 135, 831, 28, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4522, 168, 184, 4, 27, "Input"], Cell[4709, 174, 159, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4905, 183, 452, 13, 27, "Input"], Cell[5360, 198, 4709, 150, 206, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10106, 353, 418, 11, 27, "Input"], Cell[10527, 366, 663, 18, 33, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11227, 389, 214, 6, 27, "Input"], Cell[11444, 397, 313, 10, 48, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11794, 412, 360, 11, 49, "Input"], Cell[12157, 425, 611, 19, 53, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12805, 449, 383, 11, 33, "Input"], Cell[13191, 462, 900, 30, 45, "Output"] }, Open ]], Cell[14106, 495, 383, 11, 33, "Input"], Cell[CellGroupData[{ Cell[14514, 510, 430, 10, 27, "Input"], Cell[14947, 522, 232, 6, 33, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15216, 533, 384, 10, 33, "Input"], Cell[15603, 545, 549, 19, 51, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[16189, 569, 180, 4, 27, "Input"], Cell[16372, 575, 662, 22, 44, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17071, 602, 385, 11, 33, "Input"], Cell[17459, 615, 900, 30, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18396, 650, 345, 9, 33, "Input"], Cell[18744, 661, 293, 9, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19074, 675, 252, 7, 33, "Input"], Cell[19329, 684, 204, 7, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19570, 696, 424, 13, 27, "Input"], Cell[19997, 711, 329, 10, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20363, 726, 181, 3, 27, "Input"], Cell[20547, 731, 408, 14, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20992, 750, 369, 10, 27, "Input"], Cell[21364, 762, 885, 29, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[22286, 796, 152, 3, 27, "Input"], Cell[22441, 801, 3726, 112, 234, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26204, 918, 519, 12, 27, "Input"], Cell[26726, 932, 10872, 189, 238, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[37635, 1126, 463, 11, 27, "Input"], Cell[38101, 1139, 542, 17, 33, "Output"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)