2018 Metric Cones, N-body collisions, and Marchal's lemma

Blow-Up, Homotopy and Existence for Periodic Solutions of the Planar Three-Body Problem appeared in

2017 (ARXIV VERSION) Free time minimizers for the planar three-body problem with Rick Moeckel and Hector Sanchez Morgado, final version in Celestial Mechanics and Dynamical Astronomy, Vol. 130, no. 3, (2018)

2016 Constructing the Hyperbolic Plane as the reduction of a three-body problem appeared, Regular and Chaotic Dynamical Systems, Issue 6 Vol. 22 (2017). ; see also (Springer link)

Lagrangian Relations and Linear Point Billiards with Jacques Féjoz and Andreas Knauf ; appeared: Nonlinearity, 14 February 2017, Volume 30, Number 4

No Hyperbolic Pants for the Planar Four-Body Problem or at Pacific Journal with Connor Jackman. Pacific Journal of Mathematics 280-2 (2016), 401--410. DOI 10.2140/pjm.2016.280.401

2015

Syzygies in the two center problem with Holger Dullin.

Blow-up for realizing homotopy classes in the three-body problem (expository) for a school/conference held at CIMAT in Feb 2015

The Three-Body Problem and the Shape Sphere or here Amer. Math. Monthly, v 122, no. 4, pp 299-321 , April 2015.

Sard Property for the Endpoint Map on some Carnot Groups with Enrico Le Donne, Alessandro Otazzi, Pierre Pansu, and Davide Vittone. to appear, (2016?) Annales de l'Institut Henri Poincare / Analyse non lineaire.

2014

Realizing All Reduced Syzygy Sequences in the Planar Three-Body Problem also in Nonlinearity appeared, Nonlinearity 28 (2015) 1919-1935

Who's afraid of the Hill boundary? -conjugate loci clustering at the boundary (arXiv original) or . published version . SIGMA 10 (2014), 101, 11 pages;

2013

MICZ-Kepler= Dynamics on the Cone over the Rotation Group . Regular and Chaotic Dynamics November 2013, Volume 18, Issue 6, pp 600-607 (2013).

2012

Keplerian Dynamics on the Heisenberg Group and Elsewhere with Corey Shanbrom

Poincare y el problem de N-cuerpos with Gil Bor. Miscelanea matematica de la Sociedad Matematica Mexicana, May issue, n. 57 `extraordinario' ( 2013).

Symmetric Regularization, Reduction, and Blow-Up of the Planar Three-Body Problem with Rick Moeckel. Pac. J. Math. , Vol. 262, No. 1, (2013), 129-189.

Remembering Jerry (one contribution of many) ed. T. Ratiu, A. Weinstein, Notices AMS, (2012).

2011

From Brake to Syzygy . with Rick Moeckel and Andrea Venturelli. Archive for Rational Mechanics and Analysis; 204(3):1009-1060, (2012).

2009

Points and Curves in the Monster Tower (Memoirs of the AMS, 2009) or : here , with M. Zhitomirskii.

Curve Singularities and Monster / Semple Towers with Alex Castro

2008

Resolving Singularities Using Cartan's Prolongation with V. Swaminathan and M. Zhitomirskii, Journal of Fixed Point Theory and Applications (Arnol'd volume);v. 3., no. 2, Sept 2008 (alternatively: through Springer)

The Chains of Left-invariant CR-structures on SU(2) with Alex Castro; Pac. J. Math. , vol. 238, no. 1, 41-71,

Making the moon reverse its orbit: stuttering in the planar three body problem with Sam Kaplan and Mark Levi. Discrete and Continuous Dynamical Systems series B, ( Simófest issue), vol. 10, no. 2/3, 2008.

Exact identities for nonlinear wave propagation (with Duncan Ralph and Onuttom Narayan) Phys Rev E., v 77, 056219, May

2007

Dynamical Bias in the Coin Toss with Persi Diaconis and Susan Holmes

May 1, SIAM Review, Vol. 49,No . 2,pp . 211, 2007.

The zero angular momentum three-body problem: all but one solution has syzygies Erg. Th. and Dyn. Systems. v 27, no 6, 2007; pp. 1933-1946

(previously listed in 2006 as ``The only syzygy-free solution is Lagrange's'' ; completes the results of `Infinitely Many Syzygies') [older ref: Older version, w different title here ]

2006

G2 and the `Rolling Distribution' with Gil Bor; appeared : L'Enseignement Mathematique, (2) 55 ; (2009) 157-196.

Or : essentially the same via Gil's page. Rotational Invariant Operators Based on Steerable Filter Banks with Alex Castro, Roberto Manduchi, and X. Shi.

IEEE Signal Processing Letters, v. 13, no 11, Nov. 2006

Seifert's paper on brake orbits translated from the German by Bill McCain. *NOTE*! I did not write this, but I keep misplacing it and wanting to reread it. Thanks :Bill.

2005

Rotating Eights I: the three Gamma_i families with A. Chenciner, J. Fejoz; Nonlinearity 18 (2005) 1407-1424.

also available from NONLINEARITY [IOP]

Convexity of the Eight with T. Fujiwara; Pacific J. Math., Vol. 219, No. 2, Apr 2005, p. 271-284,

also available directly from: Pacific Journal of Mathematics

Hyperbolic Pants fit a three-body problem (draft; april 24, 2004, ps only for now) Ergodic Theory and Dynamical Systems, Volume 25, - June 2005, 921-947.

Nonholonomic systems via moving frames ... Chaplygin with Kurt Ehlers, Jair Koiller, and Pedro M. Rios, appeared in the 60th bday vol for Weinstein, titled `The Breadth of Symplectic and Poisson Geometry',Birkhauser, Prog in Math series, 2005

2003

Symmetry in Mechanics: A Gentle, Modern Introduction, by Stephanie Singer, American Math. Monthly, April, 2003.

2002

Infinitely Many Syzygies Archives for Rational Mechanics, v. 164 (2002), no. 4, 311--340, 2002.

Momentum maps and geometric phases (with J. Koiller,W. Earnest, Joaquin Delgado, K. Ehlers, T. Stuchi, Maria de Fatima Almeida) in Classical and celestial mechanics, (Recife, 1993/1999), 281--349, Princeton Univ. Press,

2001

A new solution to the three-body problem Notices of the American Mathematical Society, 471-481, May, 2001.

Action spectrum and collisions in the planar three-body problem (pdf) , Contemporary Math. vol. 292 (Celestial Mechancics), American Math. Society, Providence, Rhode Island, 2002.

Simple choreographies of N bodies: a preliminary study (pdf) with Alain Chenciner, Joseph Gerver, Richard Montgomery, and Carles Simó, appeared in Geometry, Mechanics, and Dynamics, volume in honor of the 60th birthday of J.E. Marsden, P. Newton, P. Holmes, A. Weinstein, ed. , Springer-Verlag, 2002.

Geometric approach to Goursat flags (with M. Zhitomirskii), Ann. Inst H. Poincare Anal. Non Lin\'eare, vol. 12, no. 4, 459-493, 2001.

2000

A remarkable periodic solution of the three-body problem in the case of equal masses, w/ Chenciner, Annals, v. 152, 881-901, Nov 2000.

Geometric quantization and no-go theorems (with V. Ginzburg) , Banach Center Publ. vol. 51, (Poisson Geometry), Polish Acad. Sci, Warsaw, 2000.

Low Reynolds number swimming in two dimensions (with A. Cherman, Joaquin Delgado, F. Duda,K. Ehlers, J. Koiller) in Hamiltonian systems and celestial mechanics (Patzcuaro, 1998)' , 32--62, World Sci. Monogr. Ser. Math., 6, World Sci. Publishing, River Edge, NJ, 2000.

review of M. Gromov's "Carnot-Caratheodary Space seen within", Featured Math Review on Math-Sci Net, May 2000.

Direct Method in the Calc. of Var'ns (unpublised undergrad notes, inspired by the Eight work)

1999

Figure 8s with 3 bodies Unpublished initial work which helped lead to `A remarkable periodic solution..' in 2000 with Chenciner. Of interest due to some ideas, notably using energy to prove collision times are isolated, that are not widely known or accessible elsewhere, and perhaps as `science history'.

Engel Deformations and Contact Structures , Amer. Math. Soc. Transl.,ed. Eliashberg and Weinstein, (2) vol 196, 103-117, 1999.

1998

The N-body problem, the braid group, and action-minimizing periodic orbits, Nonlinearity, vol. 11, no. 2, 363-376, 1998.

1997

Characteristic Classes for the Degenerations of Two-Plane Fields in Four Dimensions , with B. Shapiro and M. Kazarain. Pac. J. Math., vol. 179, no. 2, 355-370, 1997.

A nonintegrable sub-Riemannian geodesic flow on a Carnot group.(pdf) with M. Shapiro and A. Stolin. J. Dyn. Control Systems, v. 3 no. 4, 519--530, 1997.

1996

The geometric phase of the three-body problem. (pdf) Nonlinearity, v. 9, 1341-1360, 1996.

Introduction to a paper of M.Z. Shapiro: Homotopy theory in Control (ps) , in Nonsmooth analysis and geometric methods in deterministic control, The IMA Vol. Math. Appl. vol. 78, Springer-Verlag, 1996.

Do cyanobacteria swim using travelling waves? with K. Ehlers, A. Samuel, and H. Berg. Proc. Nat. Acad. , v. 93, Aug. 1996.;pp. 8340-8343.

1995

Hearing the Zero Locus of a Magnetic Field. (pdf) Communications Math. Physics, v. 168 , no. 3, 651-675, 1995.

A Survey of Singular Curves in Subriemannian Geometry (pdf), vol. 1, Journal of Dynamical and Control Systems, 1995.

1994

Abnormal Minimizers , SIAM J. Control and Optimization, vol. 32, no. 6, pp. 1605-1620, 1994.

Singular Extremals on LIe Groups Math. Control Signals Systems, vol. 7, no. 3, 217-234, 1994

1993

Generic Distributions and Lie Algebras of Vector Fields in J. Diff. Eq. , v. 103, pp. 387-393, 1993.

Gauge Theory of the Falling Cat (pdf) in `Dynamics and Control of Mechanical Systems; The falling cat and related problems, v. 1, Fields Institute Communications, ed. M. Enos, AMS pub., 1993. (detailed analysis of the Kane-Scher model cat.)

Nonholonomic Control and Gauge Theory (pdf) in `Nonholonomic Motion Planning', edited by Li and Canny, Kluwer Acad. Pub. , 1993. contains a dictionary between control theory.

The structure of optimal controls for a steering problem. (pdf) with Shankar Sastry. in selected papers from the 2nd IFAC Symposium, (Nonlinear Control Systems Design 1992) Ed. by M. Fleiss, Pergamon Press, UK, 1993.

1991

How much does the rigid body rotate? A Berry's phase from the 18th century American J. Physics, v. 59, no. 5, May 1991, pp. 394-398

Optimal Control of Deformable Bodies and Its Relation to Gauge Theory in

1990

The isoholonomic problem and some of its applications (pdf) Comm. Math. Phys., 1990, v. 128, pp 565-592.

Heisenberg and isoholonomic inequalities. Symplectic geometry and mathematical physics (Aix-en-Provence, 1990), 303--325, Progr. Math., 99, Birkhauser, (a conference proceedings in honor of Souriau)

Cartan-Hannay-Berry Phases and Symmetry , with J. Marsden and T. Ratiu, Contemp. Math. , AMS, vol. 97, 279-296, 1989.

1988

The Connection Whose Holonomy is the Classical Adiabatic Angles... Comm. Math. Phys. v. 120, 269-2294.

Shortest Loops with a Given Holonomy MSRI preprint

1987

Hamiltonian Structure of Modulation Equations for Sine-Gordon with N. Ercolani, G. Forest, and D. McLaughlin, Duke Math Journal, vol. 55 no. 4, 949-983, 1987.

1986

The bundle picture in mechanics (pdf) PhD thesis, UC Berkeley, Mathematics

The Hamiltonian Structure for Dynamic Free Boundary Value Problems with D.Lewis, J. Marsden, and T. Ratiu, Physica D ,391-404 , 1986

Covariant Poisson Brackets for Classical Fields with J. Marsden, P.J. Morrison, and W.B. Thompson, Annals of Physics , v. 169, 29-47, 1986

1985

Analytic Proof of Chaos in the Leggett Equations for Superfluid He3 (pdf) J. Low Temp. Phys, vol. 58, no. 5/6, 417-423, 1985.

1984

Canonical Formulations of a Particle in a Yang-Mills Field and Wong's Equations (pdf) Lett. Math Phys., vol. 8, 59-67, 1984.

1983

The Structure of Reduced Cotangent Bundles for Non-Free Group Actions Preprint 143 of the U.C. Berkeley Center for Pure and Applied Math, 1983.