2008
<br>


<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/Monster-April-08.pdf'> 
Points and Curves in the Monster Tower </A>
with M. Zhitomirskii. resubmitted to Memoirs of the AMS; April 08 version
<br>
** new and much improved ** 
2007 
<br>
<br>
 <A HREF='http://front.math.ucdavis.edu/0711.2555'>
The Chains of Left-invariant CR-structures on SU(2) </A>
with Alex Castro 
<br>

 <A HREF='http://count.ucsc.edu/~rmont/papers/coinSIAM.pdf'> 
Dynamical Bias in the Coin Toss </A>
with  Persi Diaconis and <A HREF='http://www-stat.stanford.edu/~susan'>
Susan Holmes </A>
<br>
May 1,  SIAM Review, Vol. 49,No . 2,pp . 211
<br>
<br>


<br>
2006

<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/R9A.pdf'> 
G_2 and the `Rolling Distribution' </A>
with Gil Bor.
<br>
<br>


<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/S10.pdf'> 
Making the moon reverse its orbit: stuttering in 
the planar three body problem  </A>
with Sam Kaplan and Mark Levi. Submitted to  the  Simofest conference
<br>
<br>


<br>
<A HREF='http://ieeexplore.ieee.org/iel5/97/36038/01707735.pdf? 
isnumber=36038&prod=JNL&arnumber=1707735&arSt=+684&ared=+687&arAuthor= 
+Shi%2C+X.%3B++Ribeiro+Castro%2C+A.L.%3B++Manduchi%2C+R.%3B+ 
+Montgomery%2C+R.'>  Rotational Invariant Operators Based on Steerable Filter Banks </A>
with Alex Castro, Roberto Manduchi, and X. Shi. <br>IEEE Signal Processing Letters, v. 13, no 11, Nov. 2006
<br>

<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/Monster-final.pdf'> 
Points and Curves in the Monster Tower </A>
with M. Zhitomirskii. Submitted to Memoirs of the AMS
<br>
<br>

<A HREF='http://front.math.ucdavis.edu/math.DS/0601269'>
The only syzygy-free solution is Lagrange's </A>
(a preprint completing the results begun in  `Infinitely Many Syzygies')

<br>
<br>
2005
<br>


<A HREF='http://www.math.jussieu.fr/~fejoz/rotatingEights.pdf'>
Rotating Eights I: the three Gamma_i  families
</A> with
A. Chenciner, J. Fejoz; 
Nonlinearity 18 (2005) 1407-1424.
<br>
<A HREF='http://www.iop.org/EJ/abstract/0951-7715/18/3/024/'>
also available from NONLINEARITY [IOP]
</A>

<br>
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/convexityFinal.pdf'> 
Convexity of the Eight
</A> with T. Fujiwara;  Pacific J. Math.,
Vol. 219, No. 2, Apr 2005, p. 271-284,
<br>
also available directly from:
<A HREF='http://pjm.math.berkeley.edu/2005/219-2/index.html'>
Pacific Journal of Mathematics </A>

<br>
<br>

<A HREF='http://count.ucsc.edu/~rmont/papers/pantsC.ps'>
Hyperbolic Pants fit a three-body problem (draft; april 24, 2004, ps only for now)
</A>
Ergodic Theory and Dynamical Systems,
Volume 25,
 - June 2005, 921-947.
<br>
<br>

 <A HREF='http://count.ucsc.edu/~rmont/papers/Chaplygin.pdf'> 
Nonholonomic systems via moving frames ... Chaplygin </A>
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
<br>

2003


<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/Symm_in_Mech_Review.PDF'>
Symmetry in Mechanics: A Gentle, Modern Introduction,
by Stephanie Singer, </A>  American Math. Monthly, April, 2003. 

<br>
<br>

2002
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/LeviS.pdf'>
  Infinitely Many Syzygies (pdf)</A>
 Archives for Rational Mechanics, v. 164 (2002), no. 4, 311--340, 2002. 
<br>
<tab> <A HREF='http://count.ucsc.edu/~rmont/papers/LeviR.ps'>
   ps version </A>  and  
 <A HREF='http://count.ucsc.edu/~rmont/papers/LeviRpics.ps'>
accompanying figures  </A>

<br>
<br>

<A HREF='http://count.ucsc.edu/~rmont/papers/Momentum_Maps.PDF'>
Momentum maps and geometric phases </A>
 (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,
 

<br>
<br>

2001

<br>
<A HREF='http://www.ams.org/notices/200105/fea-montgomery.pdf'>
 A new solution to the three-body problem </A>
Notices of the American Mathematical Society, 471-481, May, 2001. 
<br>


<br>
<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/forSaari.pdf'>
 Action spectrum and collisions in the planar three-body problem
(pdf) </A>,
 Contemporary Math. vol. 292 (Celestial Mechancics),
American Math. Society, Providence, Rhode Island, 2002.

<br>
<br>

<A HREF='http://www.imcce.fr/Equipes/ASD/preprints/prep.2001/CGMS.pdf'>
Simple choreographies of N bodies: a preliminary study (pdf)</A> with
              Alain Chenciner, Joseph Gerver, Richard Montgomery, and Carles Simo,
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.

<br>
<br>

<A HREF='http://count.ucsc.edu/~rmont/papers/goursat.pdf'>
Geometric approach to Goursat flags  </A> (with M. Zhitomirskii),
Ann. Inst H. Poincare Anal. Non Lin\'eare, vol. 12, no. 4, 
459-493, 2001.
<br>


<br>
<br>
<br>

2000
<br>

<A HREF='http://www.arxiv.org/abs/math.DS/0011268'>
A remarkable periodic solution of the three-body problem
in the case of equal masses</A>, 
with A. Chenciner, Annals of Mathematics,  v. 152, 881-901, Nov.  2000.
<br>
<br>

<A HREF= 'http://count.ucsc.edu/~rmont/papers/no_go.PDF'>
Geometric quantization and no-go theorems </A>
(with V. Ginzburg) , Banach Center Publ. vol. 51, (Poisson Geometry),
Polish Acad. Sci, Warsaw, 2000.

<br>
<br>

<A HREF='http://count.ucsc.edu/~rmont/papers/Low_Reynolds.PDF'>
Low Reynolds
number swimming in two dimensions </A>
 (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. 

<br>
<br>

<A HREF='http://count.ucsc.edu/~rmont/papers/featured_review.pdf'>
 review of M. Gromov's
"Carnot-Caratheodary Space seen within",
</A>
Featured Math Review on Math-Sci Net, May 2000.
<br>
<br>
<br>

1999

<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/deform12.ps'>
Engel Deformations and Contact Structures </A>,  Amer. Math. Soc.
Transl.,ed. Eliashberg and Weinstein,  (2) vol 196, 103-117, 1999.

<br>
<br>
<br>

1998

<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/NbdyBraids.pdf'>
The N-body problem, the braid group, and action-minimizing
periodic orbits,
</A>
 Nonlinearity, vol. 11, no. 2, 363-376, 1998.



<br>
<br>
<br>
1997

<br>

 <A HREF='http://count.ucsc.edu/~rmont/papers/CarnotFlow.pdf'>
A nonintegrable sub-Riemannian geodesic flow on a Carnot group.(pdf)</A>
with M.  Shapiro and A. Stolin, J. Dyn. Control Systems,  v. 3  no. 4, 519--530, 1997.


<br>

<br>
<br><br>
1996


<br>

 <A HREF='http://count.ucsc.edu/~rmont/papers/geometricphase.pdf'>
The geometric phase of the three-body problem. (pdf)</A>
Nonlinearity, v. 9, 1341-1360, 1996.

<br>
<br>

<A HREF='http://count.ucsc.edu/~rmont/papers/mshap3.ps'>
Introduction to a paper of M.Z. Shapiro: Homotopy theory in
Control (ps) </A>, in Nonsmooth analysis and geometric methods in
deterministic control, The IMA Vol. Math. Appl. vol. 78, Springer-Verlag,
1996.

<br> <br> <br>

1995 
<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/zerolocus.PDF'>
Hearing the Zero Locus of a Magnetic Field. (pdf)
</A>
Communications Math. Physics, v. 168 , no. 3, 651-675,
1995.
 <br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/hearing.ps'>
<tab> postscript version  </A>
<br>
<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/surveySR.pdf'>
A Survey of Singular Curves in Subriemannian Geometry (pdf)</A>, vol.
1, Journal of Dynamical and Control Systems, 1995.

<br>
<br>
<br>

1994

<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/abnormMin.ps'>
Abnormal Minimizers
</A>,  SIAM J. Control and Optimization,
vol. 32, no. 6, pp. 1605-1620, 1994.

<br>
<br>

<A HREF='http://count.ucsc.edu/~rmont/papers/singular_extremals.pdf'>
Singular Extremals on LIe Groups
</A>
Math. Control Signals Systems, vol. 7, no. 3,
217-234, 1994
<br>
<br>
<br>

1993
<br>
 
<br>

 <A HREF='http://count.ucsc.edu/~rmont/papers/cat.PDF'>
Gauge Theory of the Falling Cat
 (pdf)</A>
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.)
<br>
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/dictionary.PDF'>
Nonholonomic Control and Gauge Theory
 (pdf)</A>
in `Nonholonomic Motion Planning',
 edited by Li and Canny, Kluwer Acad. Pub.
, 1993.
contains a dictionary between control theory.

<br>
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/w_Sastry.pdf'>
The structure of optimal controls for a steering problem. (pdf)</A>
with Shankar Sastry. in selected papers
from the 2nd IFAC Symposium, (Nonlinear Control
Systems Design 1992) Ed. by M. Fleiss, Pergamon Press,
UK, 1993.

<br> <br> <br>
1992
<br>
<br>
<br>
1991
<br>
<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/rigid_body.pdf'>
How much does the rigid body rotate?  A Berry's phase from the 18th century
</A>
American J. Physics,
v. 59, no. 5, May 1991, pp. 394-398
<br>
<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/Montgomery1993.pdf'>
Optimal Control of Deformable Bodies and Its Relation to Gauge Theory
</A>
in <bf> The Geometry of Hamiltonian Systems </bf>,
Tudor Ratiu, ed., MSRI Publications, vol. 22, Springer-Verlag, 1991 
<br>
<br> 

 1990
<br>
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/Montgomery1990.pdf'>
The isoholonomic problem and some of its applications
 (pdf)</A>
Comm. Math. Phys., 1990, v. 128, pp 565-592.
<br>
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/aix_Heis.pdf'>
Heisenberg and isoholonomic inequalities.</A>
Symplectic geometry and mathematical physics 
(Aix-en-Provence, 1990), 303--325, 
Progr. Math., 99, 
Birkhauser,  (a conference proceedings in honor of Souriau)
<br>
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/MarsdenMontRat_phases.pdf'>
Cartan-Hannay-Berry Phases and
Symmetry </A>,
with J. Marsden and T. Ratiu, Contemp. Math. , AMS, vol. 97, 279-296, 1989.
<br>
<br>
 1988
<br>
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/holonomy.pdf'>
The Connection Whose Holonomy is the Classical Adiabatic Angles... </A>
Comm. Math. Phys.  v. 120, 269-2294.
<br>
<br>
 1987
<br>
<A HREF='http://count.ucsc.edu/~rmont/papers/modulation87.PDF'>
Hamiltonian
Structure of Modulation Equations for Sine-Gordon</A>
with N. Ercolani, G. Forest, and D. McLaughlin,
 Duke Math
Journal, vol. 55 no. 4, 949-983,  1987.

<br>
<br>

<br>

 1986
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/thesis.pdf'>
The bundle picture in mechanics
 (pdf)</A>
PhD thesis, UC Berkeley, Mathematics

<br>

 <A HREF='http://count.ucsc.edu/~rmont/papers/freeBVprobs86.PDF'>
The Hamiltonian Structure for Dynamic Free Boundary Value Problems</A>
with D.Lewis, J. Marsden, and T. Ratiu, Physica D ,391-404 , 1986

<br>


 <A HREF='http://count.ucsc.edu/~rmont/papers/covPBs85.PDF'>
Covariant Poisson Brackets for Classical Fields</A>
with  J. Marsden, P.J. Morrison, and W.B. Thompson, Annals of Physics ,
v. 169, 29-47,  1986

<br>

<br>

 1985
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/Leggett.pdf'>
Analytic Proof of Chaos in the Leggett Equations for
Superfluid He3
 (pdf)</A>
 J. Low Temp. Phys, vol.  58, no. 5/6, 417-423, 1985.

<br>

<br>
 1984
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/Wong.pdf'>
Canonical Formulations of a Particle in a Yang-Mills Field
and Wong's Equations
 (pdf)</A>
 Lett. Math Phys., vol. 8, 59-67, 1984.

<br>
<br>
 1983
<br>
 <A HREF='http://count.ucsc.edu/~rmont/papers/reducedcotgt83.PDF'>
The Structure of Reduced Cotangent Bundles for Non-Free Group Actions  </A>
 Preprint 143 of the U.C. Berkeley Center for Pure and
Applied Math, 1983.