Cyclicity of chaotic attractors in one-dimensional discontinuous maps
A chaotic attractor may consist of some number of bands (disjoint connected subsets). In continuous maps multi-band chaotic attractors are cyclic, that means every generic trajectory visits the bands in the same order. We demonstrate that in discontinuous maps multi-band chaotic attractors may be acyclic. Additionally, a simple criterion is proposed which allows to distinguish easily between cyclic and acyclic chaotic attractors. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.
chaotic attractors discontinuous maps piecewise smooth maps