Katok formula for the induced measure-theoretic entropy. Issue 2 (3rd April 2018)

• Record Type: Journal Article
• Authors: Xing, Zhitao; Chen, Ercai; Yin, Zheng
• Is Part Of: Dynamical systems. Volume 33:Issue 2(2018)
• Page Start: 195
• Page End: 206
• Publication Date: 2018-04-03
• Subjects: Dynamical system -- measure-theoretic entropy -- Katok formula; 37A35 -- 37B40; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2017.1329402
• Languages: English
• ISSNs: 1468-9367

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.