Katok formula for the induced measure-theoretic entropy |
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| Authors: | Zhitao Xing Ercai Chen |
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| Affiliation: | 1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, P.R. China;2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, P.R. China;3. School of Mathematical Sciences, Nanjing Normal University, Nanjing, P.R. China;4. Center of Nonlinear Science, Nanjing University, Nanjing, P.R. China |
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| Abstract: | Entropy is undoubtedly one of the most essential characteristics of dynamical systems. In this article, we define a topological version of the induced measure-theoretic entropy and obtain its Katok entropy formula. We show that the induced measure-theoretic entropy coincides with Hausdorff dimension of the ergodic measure in a symbolic space and the BS dimensions of the ergodic measures can be characterized by the induced measure-theoretic entropies. As an application, we give a variational principle of the BS dimension by the induced measure-theoretic entropy. |
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| Keywords: | Dynamical system measure-theoretic entropy Katok formula |
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