Periodic Solutions of Symmetric Hamiltonian Systems
This paper is devoted to the study of periodic solutions of a Hamiltonian system z ˙ ( t ) = J ∇ H ( z ( t ) ) , where H is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a neighborhood of non-isolated critical points of H which form orbits of the group ac...
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| Veröffentlicht in: | Archive for rational mechanics and analysis 2020-08, Vol.237 (2), p.921-950 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | This paper is devoted to the study of periodic solutions of a Hamiltonian system
z
˙
(
t
)
=
J
∇
H
(
z
(
t
)
)
, where
H
is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a neighborhood of non-isolated critical points of
H
which form orbits of the group action. We prove a Lyapunov-type theorem for symmetric Hamiltonian systems. |
|---|---|
| ISSN: | 0003-9527 1432-0673 |
| DOI: | 10.1007/s00205-020-01522-6 |