On relative normal modes

Details On relative normal modes On relative normal modes

1999-01-22

arxiv.org/abs/math/9901102v1

Mathematics

Symplectic Geometry

5 pages, to appear in C.R. Acad. Sci. Paris, t. 328, S'erie I, 1999

Scientific paper

10.1016/S0764-4442(99)80181-5

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 perodic 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.

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