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|
|Number of pages||5|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|Publication status||Published - Mar 1997|