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

TL;DR

This paper introduces a topological approach using covering relations to prove the existence of infinitely many symmetric periodic orbits in systems with reversing symmetry, demonstrated on a four-dimensional reversible map.

Contribution

The paper develops a novel topological method based on covering relations to establish symmetric periodic orbits in reversible systems, extending previous techniques.

Findings

Proves existence of infinite symmetric periodic orbits

Applies method to a four-dimensional reversible map

Demonstrates effectiveness of topological approach

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.