Hamiltonian Systems and Celestial Mechanics (HAMSYS-98) : proceedings of the III International Symposium : Patzcuaro, Michoacan, Mexico, 7-11 December 1998

373 Pages·2000·23.203 MB·English

by  Delgado, J.

World Scientific Monograph Series
in Mathematics - Vol. 6
Hamiltonian Systems
and Celestial Mechanics
(HAMSYS-98)
Proceedings of the
III International Symposium
editors
J. Delgado, E. A. Lacomba
E. Perez-Chavela &
J. Llibre
World Scientific
Hamiltonian Systems and
Celestial Mechanics
(HAMSYS-98)
World Scientific Monograph Series in Mathematics
Eds. Ron Donagi (University of Pennsylvania), Rafael de la Llave (University of Texas) and
Mikhail Shubin (Northeastern University)
Published
Vol. 1: Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's
Integral and the Regularity of Area-Minimizing Rectifiable Currents up to
Codimension 2
Eds. V. Scheffer and J. £ Taylor
World Scientific Monograph Series
in Mathematics - Vol. 6
Hamiltonian Systems and
Celestial Mechanics
(HAMSYS-98)
Proceedings of the
III International Symposium
Patzcuaro, Michoacan, Mexico 7-11 December 1998
editors
J. Delgado, E. A. Lacomba, E. Perez-Chavela
Universidad Autonoma Metropolitana-Iztapalapa, Mexico
J. Llibre
Universitat Autonoma de Barcelona, Spain
World Scientific
Singapore * New Jersey • London • Hong Kong
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HAMILTONIAN SYSTEMS AND CELESTIAL MECHANICS (HAMSYS-98)
Copyright © 2000 by World Scientific Publishing Co. Pte. Ltd.
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PREFACE
The papers in this volume are an outgrowth of the third "International
Symposium on Hamiltonian Systems and Celestial Mechanics", HAMSYS-98,
which was held in Patzcuaro, Michoacan, Mexico, December 7 to 11, 1998.
The proceedings of the first two symposia were published in Volumes 4 and
8 of the Advanced Series in Nonlinear Dynamics of World Scientific, under
the titles "Hamiltonian Systems and Celestial Mechanics", and "New Trends
in Hamiltonian Systems and Celestial Mechanics". The scientific organizers
were, in alphabetical order, J. Delgado (UAM-I), E.A. Lacomba, (UAM-I),
J. Llibre (UAB) and E. Perez-Chavela (UAM-I). The local organizer was J.
Mucino from IMUNAM-Morelia.
The third symposium gathered together 42 researchers (15 from Mexico
and 27 from abroad comprising 10 different countries) in addition to 10 grad­
uate students. There were 37 lectures in sessions of one hour or half an hour.
The main topics of the talks were Arnold diffusion, central configurations,
singularities in few body problems, billiards, area preserving maps, and ge­
ometrical mechanics. All speakers were invited to submit a contribution to
these proceedings. All papers that were received went through the referee-
ing process typical of a mathematical research journal and those that were
accepted form the present volume.
The symposium received generous support from CONACYT (Mexico)
grant 400200-5-1406PE and Academia Mexicana de Ciencias (Fundacion
Mexico-E.E.U.U. para la ciencia). The organization and realization of the
meeting was possible due to a lot of work on the part of a number of peo­
ple. Special thanks are due to Petra Seligman from CIC who took care of
the logistic administration of the meeting and many other things. We also
thank the economical support provided by the following institutions: From
Mexico, UAM-I, FENOMEC, IMUNAM-Morelia, FC-UNAM. From Spain:
UAB, DGICYT. And from the international institutions ICTP and UMALCA.
And last but not least, the participants at the conference must be thanked
for offering everyone a week-long intense and highly interesting mathematical
experience.
J. Delgado*, E.A. Lacomba*, J. Llibre** and E. Perez-Chavela*.
* Universidad Autonoma Metropolitana-Iztapalapa, Departamento de
Matematicas Ap. P. 55-534, Mexico D.F.
** Departament de Matematiques, Universitat Autonoma de Barcelona,
08193 Bellaterra, Barcelona, Spain.
VII
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CONTENTS
Preface vii
The Rhomboidal Charged Four Body Problem 1
F. Alfaro and E. Perez-Chavela
Planetary Rings with Shepherds 20
L. Benet and T.H. Seligman
Low Reynolds Number Swimming in Two Dimensions 32
A. Cherman, J. Delgado, F. Duda, K. Ehlers,
J. Koiller and R. Montgomery
2-Dimensional Invariant Tori for the Spatial Isosceles 3-Body Problem 63
M. Corbera and J. Llibre
The Global Flow for the Synodical Spatial Kepler Problem 74
M.P. Dantas and J. Llibre
Unbounded Growth of Energy in Periodic Perturbations of Geodesic
Flows of the Torus 90
A. Delshams, R. De La Llave and T.M. Seara
Splitting and Melnikov Potentials in Hamiltonian Systems 111
A. Delshams and P. Gutierrez
Infinity Manifolds of Cubic Polynomial Hamiltonian Vector
Fields with 2 Degrees of Freedom 138
M. Falconi, E.A. Lacomba and J. Llibre
IX