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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.
Acknowledgment
We would like to thank the referees for very useful comments and helpful suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
National Natural Science Foundation of China [grant number 11671208], [grant number11431012], [grant number11401581].