Open AccessPeriodic solutions to symmetric Newtonian systems in neighborhoods of orbits of equilibria
Author(s) -
Anna Gołębiewska,
Marta Kowalczyk,
Sławomir Rybicki,
Piotr Stefaniak
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022085
Subject(s) - equivariant map , mathematics , orbit (dynamics) , pure mathematics , periodic orbits , generalization , bifurcation , lyapunov function , dynamical systems theory , mathematical analysis , physics , nonlinear system , quantum mechanics , engineering , aerospace engineering
The aim of this paper is to prove the existence of periodic solutions to symmetric Newtonian systems in any neighborhood of an isolated orbit of equilibria. Applying equivariant bifurcation techniques we obtain a generalization of the classical Lyapunov center theorem to the case of symmetric potentials with orbits of non-isolated critical points. Our tool is an equivariant version of the Conley index. To compare the indices we compute cohomological dimensions of some orbit spaces.