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A simple method for finding topological horseshoes. (English) Zbl 1188.37035
Summary: 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 Poincaré 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 Hénon 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.
MSC:
37D45Strange attractors, chaotic dynamics
37E05Maps of the interval (piecewise continuous, continuous, smooth)
37B10Symbolic dynamics