Abstract
It was known to Poincaré that a non-degenerate periodic orbit in a Hamiltonian system persists to nearby energy-levels. In this Note, we consider the analogous problem for relative periodic orbits in symmetric Hamiltonian systems. We show that non-degenerate relative periodic orbits also persist when shifting to nearby values of the energy-momentum map, under the hypothesis that the group of symmetries acts freely.
| Translated title of the contribution | Persistence of relative periodic orbits in symmetric Hamiltonian systems |
|---|---|
| Original language | French |
| Pages (from-to) | 553-558 |
| Number of pages | 5 |
| Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
| Volume | 324 |
| Issue number | 5 |
| Publication status | Published - Mar 1997 |