A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems

Authors
Ortega, JP Ratiu, TS
Citation
Jp. Ortega et Ts. Ratiu, A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems, J GEOM PHYS, 32(2), 1999, pp. 131-159
Citations number
48
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF GEOMETRY AND PHYSICS
ISSN journal
03930440 → ACNP
Volume
32
Issue
2
Year of publication
1999
Pages
131 - 159
Database
ISI
SICI code
0393-0440(199912)32:2<131:ADCFTS>2.0.ZU;2-4
Abstract
The classical Dirichlet criterion on the stability of equilibria in Hamilto nian systems is generalized to the orbital stability of periodic orbits. Th e result obtained is adapted to the study of the stability of relative peri odic orbits in Hamiltonian systems with symmetry that lie at regular level sets of the corresponding momentum map. (C) 1999 Elsevier Science B.V. All right reserved. Subj. Class.: Dynamical systems 1991 MSG: 34D35; 58F05.