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Hamiltonian Dynamics and Celestial Mechanics
Edited by: Donald G. Saari and Zhihong Xia, Northwestern University, Evanston, IL

Contemporary Mathematics
1996; 240 pp; softcover
Volume: 198
ISBN-10: 0-8218-0566-5
ISBN-13: 978-0-8218-0566-4
List Price: US$93
Member Price: US$74.40
Order Code: CONM/198
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See also:

Chaotic Elections! A Mathematician Looks at Voting - Donald G Saari

Celestial Mechanics: Dedicated to Donald Saari for his 60th Birthday - Alain Chenciner, Richard Cushman, Clark Robinson and Zhihong Jeff Xia

This book contains selected papers from the AMS-IMS-SIAM Joint Summer Research Conference on Hamiltonian Systems and Celestial Mechanics held in Seattle in June 1995.

The symbiotic relationship of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems.

As one of the few books that addresses both Hamiltonian systems and celestial mechanics, this volume offers emphasis on new issues and unsolved problems. Many of the papers give new results, yet the editors purposely included some exploratory papers based on numerical computations, a section on unsolved problems, and papers that pose conjectures while developing what is known.


  • Open research problems
  • Papers on central configurations


Graduate students, research mathematicians, and physicists interested in dynamical systems, Hamiltonian systems, celestial mechanics, and/or mathematical astronomy.

Table of Contents

  • J. M. Cors and J. Llibre -- Qualitative study of the parabolic collision restricted three-body problem
  • D. G. Saari and Z. Xia -- Singularities in the Newtonian \(n\)-body problem
  • P. H. Rabinowitz -- A variational approach to multibump solutions of differential equations
  • C. Robinson -- Melnikov method for autonomous Hamiltonians
  • N. K. Swami -- Exponentially small transversality in the rapidly forced pendulum
  • S. R. Kaplan -- The collinear one-bumper two-body problem
  • P. W. Lindstrom -- Limiting mass distributions of minimal potential central configurations
  • A. Albouy -- The symmetric central configurations of four equal masses
  • E. Perez-Chavela, D. G. Saari, A. Susin, and Z. Yan -- Central configurations in the charged three body problem
  • M. Kummer -- Reduction in the rotating Kepler problem and related topics
  • M. Falconi and E. A. Lacomba -- Asymptotic behavior of escape solutions of mechanical systems with polynomial potentials
  • Q. Wang -- More on the heteroclinic orbits for the monotone twist maps
  • T. R. Young -- Transition maps of homoclinic orbits and resonances near bifurcations of circle maps
  • X. Liao, D. G. Saari, and Z. Xia -- Resonance transition and instabilities; A numerical study of the restricted three-body problem
  • S. R. Kaplan, R. Cushman, S. Hu, J. Llibre, C. McCord, D. G. Saari, and Z. Xia -- Directions of Hamiltonian dynamics and celestial mechanics
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