Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 16239, 9 pages
Research Article

A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System

Qingdu Li1 and Xiao-Song Yang2

1Institute for Nonlinear Systems, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 13 October 2006; Accepted 14 November 2006

Copyright © 2007 Qingdu Li and Xiao-Song Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a three-dimensional topological horseshoe in the hyperchaotic generalized Hénon map. It looks like a planar Smale horseshoe with an additional vertical expansion, so we call it 3D Smale horseshoe. In this way, a computer assisted verification of existence of hyperchaos is provided by means of interval analysis.