A New Proof for the Existence of Topological Horseshoe in Chen's Attractor

Abstract

Based on the well-known topological horseshoe theorem, a new rigorous computer-assisted proof for the existence of topological horseshoe in Chen’s attractor is given. An appropriate Poincaré section of Chen’s attractor is chosen to obtain the corresponding Poincaré map which is proved to be semi-conjugate to a 2-shift map. This implies that Chen’s attractor has positive topological entropy, thus in this sense it is chaotic. The method used is somewhat simpler and more convenient than the classical Ši’lnikov method.