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Research Article | Open Access

Periodic solutions to symmetric Newtonian systems in neighborhoods of orbits of equilibria

Anna Gołȩbiewska, Marta Kowalczyk, Sławomir Rybicki( ), Piotr Stefaniak
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University in Toruń, PL-87-100 Toruń, ul. Chopina 12/18, Poland
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Abstract

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.

Keywords

Lyapunov center theoremsymmetric Newtonian systemsequivariant Conley indexperiodic solutionssymmetric bifurcations

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Electronic Research Archive
Volume 30 Issue 5,
May 2022
Pages 1691-1707
DOI: 10.3934/era.2022085

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Cite this article:
Gołȩbiewska A, Kowalczyk M, Rybicki S, et al. Periodic solutions to symmetric Newtonian systems in neighborhoods of orbits of equilibria. Electronic Research Archive, 2022, 30(5): 1691-1707. https://doi.org/10.3934/era.2022085

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Received: 13 August 2021
Revised: 15 January 2022
Accepted: 15 January 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)