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arXiv · 1810.09293

Symmetric Liapunov center theorem for orbit with nontrivial isotropy group

Marta Kowalczyk·Ernesto Pérez-Chavela·Sławomir Rybicki
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Abstract

In this article we prove two versions of the Liapunov 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 $\Gamma$ acting linearly on $\mathbb{R}^n.$ We look for non-stationary periodic solutions of this system in a~neighborhood of an orbit of critical points of the potential $U.$

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Marta Kowalczyk, Ernesto Pérez-Chavela, Sławomir Rybicki. 2018-10-22. Symmetric Liapunov center theorem for orbit with nontrivial isotropy group. https://arxiv.org/abs/1810.09293

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