Compactification of the energy surfaces for n bodies with A. Knauf
No Infinite Spin in the Planar n-body problem with R. Moeckel
Dropping Bodies (arXiv, in 2022) or Intelligencer version Appeared, Math. Intelligencer. Feb, 2023. <>
Geodesics in Jet Space (arxiv version, 2021) with Alejandro Bravo Doddoli. appeared: Reg and Chaotic Dyn. ; number 2 Vol. 27 (2022)
Classical n-body scattering with long-range potentials (arXiv 2020, ) or
( official version ),
with Jacques Fejoz and Andreas Knauf,
Nonlinearity , Oct. 14, 2021, Vol 34, N. 11, 8017
Evading Anderson localization in a one-dimensional conductor with
with Onuttom Narayan and Harsh Mathur. Phys Rev B, 103, 144203 – April 2021.
see also Phys Rev
Bicycle paths, elasticae and sub-Riemannian geometry
with Andrey Ardentov, Gil Bor, Enrico Le Donne, and Yuri Sachkov. In June 2021 Nonlinearity vol 34 4661--.
Chazy-Type Asymptotics and Hyperbolic Scattering for the n-Body Problem in : Arch. Rat. Mech, vol. 238, 255–297, 2020,
Oscillating about coplanarity in the 4 body problem , Inventiones, Mar. 2019,
Minimizers for the Kepler Problem (arxiv: 2019?) ,proc. in honor of Florin Diacu.
Qualitative Theory of Dynamical Systems, vol. 19, Article number: 31 (2020) .
Chains in CR geometry as geodesics of a Kropina metric with J-H. Cheng, T. Marugame and
V. Matveev ; Advances in Mathematics 350 (2019) pp. 973-999.
Metric Cones, N-body collisions, and Marchal's lemma
Blow-Up, Homotopy and Existence for Periodic Solutions of the Planar Three-Body Problem
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)
Constructing the Hyperbolic Plane as the reduction of a three-body
-with Mnëv universality added in
-as pub. in
Reg. and Chaotic Dynamical Systems , Issue 6 , v. 22 (2017).
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
Syzygies in the two center problem with Holger Dullin. Nonlinearity, (2016), Vol. 29, No. 4
Blow-up for realizing homotopy classes in the three-body problem (expository) from conference at CIMAT , Feb 2015; appeared in Geometrical Themes Inspired by the N-body Problem
Springer LNM 2204, L. Hern\'andez-LaMondea, H. Herrera , and R. Herrera editors, (2018).
DOI 978-3-319-71428-8_2; contains my perspective on McGehee blow-up
The Three-Body Problem and the Shape Sphere or
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.
Realizing All Reduced Syzygy Sequences in the Planar Three-Body Problem also in
appeared, Nonlinearity 28 (2015) 1919-1935
Who's afraid of the Hill boundary? -conjugate loci clustering at the boundary (arXiv original)
published version .
SIGMA 10 (2014), 101, 11 pages;
MICZ-Kepler= Dynamics on the Cone over the Rotation Group
. Regular and Chaotic Dynamics
November 2013, Volume 18, Issue 6, pp 600-607
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).
From Brake to Syzygy .
with Rick Moeckel and Andrea Venturelli.
Archive for Rational Mechanics and Analysis; 204(3):1009-1060, (2012).
Points and Curves in the Monster Tower (Memoirs of the AMS, 2009)
with M. Zhitomirskii.
Curve Singularities and Monster / Semple Towers
with Alex Castro
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:
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
(with Duncan Ralph and Onuttom Narayan) Phys Rev E., v 77, 056219, May
Dynamical Bias in the Coin Toss
with Persi Diaconis and
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 ]
G2 and the `Rolling Distribution' with Gil Bor; appeared : L'Enseignement Mathematique, (2) 55 ; (2009) 157-196.
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.
Rotating Eights I: the three Gamma_i families
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,
- 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
Symmetry in Mechanics: A Gentle, Modern Introduction,
by Stephanie Singer, American Math. Monthly, April, 2003.
Infinitely Many Syzygies
Archives for Rational Mechanics, v. 164 (2002), no. 4, 311--340, 2002.
ps version and
accompanying figures )
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,
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
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,
Geometric approach to Goursat flags (with M. Zhitomirskii),
Ann. Inst H. Poincare Anal. Non Lin\'eare, vol. 12, no. 4,
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.
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)
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.
The N-body problem, the braid group, and action-minimizing
Nonlinearity, vol. 11, no. 2, 363-376, 1998.
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.
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,
Do cyanobacteria swim using travelling waves? with K. Ehlers, A. Samuel, and H. Berg.
Proc. Nat. Acad. , v. 93, Aug. 1996.;pp. 8340-8343.
Hearing the Zero Locus of a Magnetic Field. (pdf)
Communications Math. Physics, v. 168 , no. 3, 651-675,
A Survey of Singular Curves in Subriemannian Geometry (pdf), vol.
1, Journal of Dynamical and Control Systems, 1995.
, 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,
Examples of Singular Reduction (with Eugene Lerman and Reyer Sjamaar), in Symplectic Geometry, ed. by D. Salomon, London Math. Society Lecture Note Ser., 192, 127-155, Cambridge University Press, 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
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
in `Nonholonomic Motion Planning',
edited by Li and Canny, Kluwer Acad. Pub.
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,
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 The Geometry of Hamiltonian Systems ,
Tudor Ratiu, ed., MSRI Pub. vol. 22, Springer-Ver., 1991
The isoholonomic problem and some of its applications
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
with J. Marsden and T. Ratiu, Contemp. Math. , AMS, vol. 97, 279-296, 1989.
Dynamics and Optimal Control of a Legged Robot in Flight Phase.
(with Zexiang Li) IEEE Int'l Conference on Robotics and Automation, pp.1816-1821, (1990)
The Connection Whose Holonomy is the Classical Adiabatic Angles...
Comm. Math. Phys. v. 120, 269-2294.
Shortest Loops with a Given Holonomy
Structure of Modulation Equations for Sine-Gordon
with N. Ercolani, G. Forest, and D. McLaughlin,
Journal, vol. 55 no. 4, 949-983, 1987.
The bundle picture in mechanics
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
Analytic Proof of Chaos in the Leggett Equations for
J. Low Temp. Phys, vol. 58, no. 5/6, 417-423, 1985.
Canonical Formulations of a Particle in a Yang-Mills Field
and Wong's Equations
Lett. Math Phys., vol. 8, 59-67, 1984.
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.