Hamiltonian dynamical systems (PDF)

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 Poincare-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.