A horseshoe with a discontinuous entropy spectrum
Dynamical Systems
2019-10-15 v1
Abstract
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 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.
Keywords
Cite
@article{arxiv.1910.05837,
title = {A horseshoe with a discontinuous entropy spectrum},
author = {Pavel Javornik and Joseph Winter and Christian Wolf},
journal= {arXiv preprint arXiv:1910.05837},
year = {2019}
}