Topological method for symmetric periodic orbits for maps with a reversing symmetry

Daniel Wilczak; Piotr Zgliczyński

doi:10.3934/dcds.2007.17.629

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2007, Volume 17, Issue 3: 629-652. Doi: 10.3934/dcds.2007.17.629

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Topological method for symmetric periodic orbits for maps with a reversing symmetry

Daniel Wilczak^1, and
Piotr Zgliczyński^2,

1.
Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Kraków
2.
Department of Computational Mathematics, Faculty of Computer Science, WSB – NLU, Zielona 27, 33-300 Nowy Sącz

Received: January 31, 2006

Revised: May 31, 2006

Published: August 2007

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Abstract

We present a topological method of obtaining the existence of infinite number of symmetric periodic orbits for systems with reversing symmetry. The method is based on covering relations. We apply the method to a four-dimensional reversible map.

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Mathematics Subject Classification: 37C25, 37C80, 65G20.

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