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Katok formula for the induced measure-theoretic entropy

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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… Click to show full abstract

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.

Keywords: induced measure; measure theoretic; entropy; formula; measure; theoretic entropy

Journal Title: Dynamical Systems
Year Published: 2018

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