A horseshoe with a discontinuous entropy spectrum

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:496

Article

Javornik, Pavel¹  Winter, Joseph²  Wolf, Christian² 

[1] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

[2] CUNY City Coll, Dept Math, New York, NY 10031 USA

关键词: Multifractal spectra;    Hyperbolicity;    Entropy spectrum;    Lyapunov exponents;    Discontinuity;   

DOI  :  10.1016/j.jmaa.2020.124811

来源: Elsevier

【 摘 要 】

We study the regularity of the entropy spectrum of the Lyapunov exponents for hyperbolic maps on surfaces. It is well-known that the entropy spectrum is a concave upper semi-continuous function which is analytic on the interior of the set of Lyapunov exponents. In this paper we construct a family of horseshoes with a discontinuous entropy spectrum at the boundary of the set of Lyapunov exponents. (C) 2020 Elsevier Inc. All rights reserved.

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