New Advances in Celestial Mechanics and Hamiltonian Systems

by Delgado, Joaquin; Lacomba, E. A.; Llibre, J.; Perez-Chavela, E.

• ISBN13: 9780306481178
• ISBN10: 0306481170
• Format: Hardcover
• Copyright: 2004-05-01
• Publisher: Plenum Pub Corp

Summary

The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects. For PhD students, this meeting offered also the opportunity of personal contact to help themselves in their own research, to call as well and promote the attention of young researchers and graduated students from our scientific community to the above topics, which are nowadays of interest and relevance in Celestial Mechanics and Hamiltonian dynamics. A glance to the achievements in the area in the last century came as a consequence of joint discussions in the workshop sessions, new problems were presented and lines of future research were delineated. Specific discussion topics included: New periodic orbits and choreographies in the n-body problem, singularities in few body problems, central configurations, restricted three body problem, geometrical mechanics, dynamics of charged problems, area preserving maps and Arnold diffusion.

Table of Contents

Preface
Drawing
Exchange and capture in the planar restricted parabolic 3-body problem	p. 1
Fitting invariant curves on billiard tables and the Birkhoff-Herman theorem	p. 29
Construction of periodic orbits in Hill's problem for C [subscript ä][superscript [greater than]] 3[superscript 4/3]	p. 37
Are there perverse choreographies?	p. 63
Blow up of total collision in the tetrahedral non-rotating four body problem	p. 77
Symbolic dynamics for transition Tori-II	p. 95
A survey on bifurcations of invariant Tori	p. 109
Perturbing the Lagrange solution to the general three body problem	p. 123
Horseshoe periodic orbits in the restricted three body problem	p. 137
Instability of periodic orbits in the restricted three body problem	p. 153
Syzygies and the integral manifolds of the spatial N-body problem	p. 169
Dynamics and bifurcation near the transition from stability to complex instability	p. 185
Invariant manifolds of spatial restricted three-body problems : the lunar case	p. 199
Path integral quantization of the sphere	p. 225
Non-holonomic systems with symmetry allowing a conformally symplectic reduction	p. 239
Index	p. 253
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