Affiliation:
1. Institute of Information Theory and Automation, v.v.i., Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, P. O. Box 18, 182 08 Prague 8, Czech Republic
Abstract
In this paper, the chaotic behavior of a set-valued mapping F : X → 2X, where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2X is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of the mapping F, it is shown that the Bernoulli system of bi-directional shifts is embedded in the sense of semiconjugacy into the image of mapping F, i.e. Smale's chaos in the set-valued system F is thereby proved.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)