Relative Entropy, Asymptotic Pairs and Chaos |
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| Authors: | Zhang Guohua |
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| Institution: | Department of Mathematics, University of Science and Technology of China Hefei, Anhui 230026, People's Republic of China ghzhang{at}mail.ustc.edu.cn |
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| Abstract: | In this paper, we prove that positive conditional entropy impliesthe existence of asymptotic pairs and scrambled sets on fibers.Moreover, we introduce the notion of conditional topologicalentropy for a subset using Bowen's definition of separated andspanning sets, and prove that the conditional topological entropyof a system relative to a factor is the supremum of conditionaltopological entropy of its scrambled sets on fibers. |
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