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Normal modes in symplectic stratified spaces

Eugene Lerman
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Abstract

We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) 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. More specifically we significantly improve a result proved earlier jointly with Tokieda (math.SG/9901102): we remove a technical hypothesis which amounted to an assumption that the symmetry group is a torus.

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Eugene Lerman. 1999-06-18. Normal modes in symplectic stratified spaces. https://arxiv.org/abs/math/9906007

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