Publication:
Periodic orbits of Hamiltonian systems and symplectic reduction

Loading...
Thumbnail Image
Full text at PDC
Publication Date
1996
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
IOP Publishing
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
The notion of relative periodic orbits for Hamiltonian systems with symmetry is discussed and a correspondence between periodic orbits of reduced and unreduced Hamiltonian systems is established. Variational principles with symmetries are studied from the point of view of symplectic reduction of the space of loops, leading to a characterization of reduced periodic orbits by means of the critical subsets of an action functional restricted to a submanifold of the loop space of the unreduced manifold. Finally, as an application, it is shown that if the symplectic form ! has finite integral rank, then the periodic orbits of a Hamiltonian system on the symplectic manifold .M; !/ admit a variational characterization.
Description
Keywords
Citation
Abraham R and Marsden J E 1978 Foundations of Mechanics 2nd edn (New York: Benjamin) Cendra H and Marsden J E 1987 Physica 27D 63 Cendra H, Marsden J E and Ibort L A 1987 J. Geom. Phys. 29 541 Fortune B 1985 Invent. Math. 81 29 Fortune B and Weinstein A 1985 Bull. Am. Math. Soc. 12 128 Freed D S 1988 J. Diff. Geom. 28 223 Gotay M J 1982 Proc. Am. Math. Soc. 84 111 Guillemin V and Sternberg S 1984 Symplectic Techniques in Physics (Cambridge: Cambridge University Press) Gotay M J and Tuynman G M 1989 Lett. Math. Phys. 18 55 Ibort A and Martínez–Ontalba C 1994 C.R. Acad. Sci. Paris Série II 318 561 Ibort A and Martínez–Ontalba C 1995 Arnold’s conjecture and symplectic reduction J. Geom. Phys. to appear Klingenberg W 1978 Lectures on Closed Geodesics (Berlin: Springer) Marsden J E 1993 Lectures on Mechanics (Cambridge: Cambridge University Press) Smale S 1970 Invent. Math. 10 305 Weinstein A 1978 Math. Z. 159 235
Collections