# Hamiltonian Dynamical Systems

Share this page *Edited by *
*Kenneth R Meyer; Donald G Saari*

This volume contains contributions by participants in the
AMS-IMS-SIAM Summer Research Conference on Hamiltonian Dynamical Systems, held
at the University of Colorado in June 1984. The conference brought together
researchers from a wide spectrum of areas in Hamiltonian dynamics. The papers
vary from expository descriptions of recent developments to fairly technical
presentations with new results. Collectively, they provide an excellent survey
of contemporary work in this area.

The field of Hamiltonian dynamics has its roots in Newton's application of
the science of dynamics to the emerging problems of orbital mechanics and in
the development of celestial mechanics. Indeed, many of the talks at the
conference emphasized topics directly concerned with such questions as the
Newtonian \(n\)-body problem, the three-body problem, and the
artificial earth satellite. Some speakers focused on those dynamical
issues—such as integrability, KAM, and extensions of the
Poincaré-Birkhoff results—that emerged from celestial mechanics
and extend to wider classes of dynamical systems.

Other topics covered include periodic orbits with variation methods, twist
and annulus maps, stable mainfold theory, almost periodic motion, and
heteroclinic and homoclinic orbits. By bringing together papers from such a
diverse range of topics, this book may serve to stimulate further development
in this area.

#### Table of Contents

# Table of Contents

## Hamiltonian Dynamical Systems

- Contents ix10 free
- Preface xi12 free
- Some qualitative features of the three-body problem 114 free
- Symmetry in n-particle systems 2336
- The charged isosceles 3-body problem 4356
- Central configurations in R2 and R3 5972
- Stable manifolds in Hamiltonian systems 7790
- Reduction of Hamiltonian systems for singular values of momentum 99112
- A variation on the Poincaré-Birkhoff theorem 111124
- An analog of Sharkovski's theorem for twist maps 119132
- Some problems on dynamics of annulus maps 135148
- Area preserving homeomorphisms of two manifolds 153166
- An Anosov type stability theorem for almost periodic systems 169182
- The prescribed energy problem for periodic solutions of Hamiltonian systems 183196
- Homoclinic and heteroclinic phenomena in some Hamiltonian systems 193206
- Exponentially small splittings of separatrices with applications to KAM theory and degenerate bifurcations 213226
- The three point vortex problem: Commutative and non-commutative integrability 245258
- On a theorem of Ziglin in Hamiltonian dynamics 259272