Topological entropy of generalized discrete dynamical system

Xiaoqian Song, Jinkui Liu, Xi Zhu

Abstract


In this paper, the authors introduce Bowen’s topological entropy for generalized discrete dynamical system. This is achieved through the consideration of the generalized spanning sets and generalized separated sets. Besides, we obtain that our definition keeps some properties which are held by the classic definition of topological entropy introduced for metric sets. Finally, we further discuss the relations of the generalized spanning set and generalized separated set between systems and their product system. These results further extend the scope of the research on discrete dynamical system and generalize the existing results to a very general case.

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How to Cite this Article:

Xiaoqian Song, Jinkui Liu, Xi Zhu, Topological entropy of generalized discrete dynamical system, Journal of Mathematical and Computational Science, Vol 2, No 4 (2012), 1116-1125

Copyright © 2012 Xiaoqian Song, Jinkui Liu, Xi Zhu. 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.

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