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RELATIVE ENTROPY, ASYMPTOTIC PAIRS AND CHAOS

Published online by Cambridge University Press:  22 February 2006

GUOHUA ZHANG
GUOHUA ZHANG
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of Chinaghzhang@mail.ustc.edu.cn
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Abstract

In this paper, we prove that positive conditional entropy implies the existence of asymptotic pairs and scrambled sets on fibers. Moreover, we introduce the notion of conditional topological entropy for a subset using Bowen's definition of separated and spanning sets, and prove that the conditional topological entropy of a system relative to a factor is the supremum of conditional topological entropy of its scrambled sets on fibers.

Keywords

37A0537A35
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 157 - 172
Copyright
The London Mathematical Society 2006

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