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January/February 2020 Symmetric Lyapunov center theorem for orbit with nontrivial isotropy group
Marta Kowalczyk, Ernesto Pérez-Chavela, Sławomir Rybicki
Adv. Differential Equations 25(1/2): 1-30 (January/February 2020).

Abstract

In this article, we prove two versions of the Lyapunov center theorem for symmetric potentials. We consider a second order autonomous system $$ \ddot q(t)=-\nabla U(q(t)) $$ in the presence of symmetries of a compact Lie group $\Gamma.$ We look for non-stationary periodic solutions of this system in a neighborhood of a $\Gamma$-orbit of critical points of the $\Gamma$-invariant potential $U.$ Our results generalize that of [13, 14]. As a topological tool, we use an infinite-dimensional generalization of the equivariant Conley index due to Izydorek, see [9].

Citation

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Marta Kowalczyk. Ernesto Pérez-Chavela. Sławomir Rybicki. "Symmetric Lyapunov center theorem for orbit with nontrivial isotropy group." Adv. Differential Equations 25 (1/2) 1 - 30, January/February 2020.

Information

Published: January/February 2020
First available in Project Euclid: 6 February 2020

zbMATH: 07198955
MathSciNet: MR4060442

Subjects:
Primary: 34C25, 37G40

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.25 • No. 1/2 • January/February 2020
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