A SIMPLE METHOD FOR FINDING TOPOLOGICAL HORSESHOES

This paper presents an efficient method for finding horseshoes in dynamical systems by using several simple results on topological horseshoes. In this method, a series of points from an attractor of a map (or a Poincare map) are firstly computed. By dealing with the series, we can not only find the approximate location of each short unstable periodic orbit (UPO), but also learn the dynamics of almost every small neighborhood of the attractor under the map or the reverse map, which is very helpful for finding a horseshoe. The method is illustrated with the Henon map and two other examples. Since it can be implemented with a computer software, it becomes easy to study the existence of chaos and topological entropy by virtue of topological horseshoe.