Mathematical Research Letters

Volume 11 (2004)

Number 3

Existence of relative periodic orbits near relative equilibria

Pages: 397 – 412



Viktor Ginzburg (University of California at Santa Cruz)

Eugene Lerman (University of Illinois at Urbana-Champaign)


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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