Periodic Solutions of Hamiltonian Systems: A Survey,
Abstract
Hamiltonian systems of ordinary differential equations model the motion of a discrete mechanical system. During the past few years there has been a considerable amount of progress in the study of periodic solutions of such systems with many new ideas and methods of solution being introduced. The purpose of this paper is to survey these recent developments and their connection with some earlier results. In particular the main results that have been obtained will be stated and an indication will be given of their proofs. A few open questions will also be mentioned. In conclusion it should be mentioned that one of the main sources of inspiration for the development of Hamiltonian mechanics was the field of celestial mechanics. In this field, one encounters Hamiltonians which possess singularities. We believe celestial mechanics is a very interesting and possibly fertile proving ground for the further development of the ideas and methods described in this study.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1979
- Accession Number
- ADA093444
Entities
People
- Paul H. Rabinowitz
Organizations
- University of Wisconsin Madison Department of Mathematics