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

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August 2007, 17(3): 629-652. doi: 10.3934/dcds.2007.17.629

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, Poland
2.	Department of Computational Mathematics, Faculty of Computer Science, WSB – NLU, Zielona 27, 33-300 Nowy Sącz, Poland

Received February 2006 Revised June 2006 Published December 2006

Abstract
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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.

Keywords: symmetric periodic orbits, reversible systems, computer assisted proofs..

Mathematics Subject Classification: 37C25, 37C80, 65G2.

Citation: Daniel Wilczak, Piotr Zgliczyński. Topological method for symmetric periodic orbits for maps with a reversing symmetry. Discrete & Continuous Dynamical Systems - A, 2007, 17 (3) : 629-652. doi: 10.3934/dcds.2007.17.629

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