**Contemporary Mathematics**

Volume: 198;
1996;
240 pp;
Softcover

MSC: Primary 70; 58;

Print ISBN: 978-0-8218-0566-4

Product Code: CONM/198

List Price: $93.00

Individual Member Price: $74.40

**Electronic ISBN: 978-0-8218-7789-0
Product Code: CONM/198.E**

List Price: $93.00

Individual Member Price: $74.40

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# Hamiltonian Dynamics and Celestial Mechanics

Share this page *Edited by *
*Donald G. Saari; Zhihong 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

#### Table of Contents

# Table of Contents

## Hamiltonian Dynamics and Celestial Mechanics

- Contents v6 free
- Preface vii8 free
- Qualitative Study of the Parabolic Collision Restricted Three-body Problem 110 free
- Singularities in the Newtonian n-body Problem 2130
- A Variational Approach to Multibump Solutions of Differential Equations 3140
- Melnikov Method for Autonomous Hamiltonians 4554
- Exponentially Small Transversality in the Rapidly Forced Pendulum 5564
- The Collinear One-bumper Two-body Problem 8796
- Limiting Mass Distributions of Minimal Potential Central Configurations 109118
- The Symmetric Central Configurations of Four Equal Masses 131140
- Central Configurations in the Charged Three Body Problem 137146
- Reduction in the Rotating Kepler Problem and Related Topics 155164
- Asymptotic Behavior of Escape Solutions of Mechanical Systems with Polynomial Potentials 181190
- More on the Heteroclinic Orbits for the Monotone Twist Maps 197206
- Transition Maps of Homoclinic Orbits and Resonances near Bifurcations of Circle Maps 207216
- Resonance Transition and Instabilities; A Numerical Study of the Restricted Three-body Problem 219228
- Directions of Hamiltonian Dynamics and Celestial Mechanics 229238

#### Readership

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