Sur les oscillations normales relatives

Translated title of the contribution: On relative normal modes

Eugene Lerman, Tadashi Tokieda

Research output: Contribution to journalArticlepeer-review

Abstract

We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. In particular, we prove that under appropriate hypotheses there exist relative periodic orbits near relative equilibria even when these relative equilibria are singular points of the corresponding moment map, i.e. when the reduced spaces are singular.

Translated title of the contributionOn relative normal modes
Original languageFrench
Pages (from-to)413-418
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume328
Issue number5
DOIs
StatePublished - Mar 1999

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On relative normal modes'. Together they form a unique fingerprint.

Cite this