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

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 Poincare section of Chen´s attractor is chosen to obtain the corresponding Poincare 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 Si´lnikov method.