Relative Nonlinear Normal Modes of Hamiltonian Systems
نویسنده
چکیده
We generalize theWeinstein-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: we remove a technical hypothesis which amounted to an assumption that the symmetry group is a torus.
منابع مشابه
Existence of Relative Periodic Orbits near Relative Equilibria
We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative version of the Moser-Weinstein theorem.
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