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

摘要

Based on the well-known topological horseshoe theorem, a new rigorous computer-assisted proof for the existence of topological horseshoe in Chenȁ9;s attractor is given. An appropriate Poincaré section of Chenȁ9;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 Chenȁ9;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 Šiȁ9;lnikov method.