Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 16239, 9 pages
A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System
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.