Mathematical Research Letters

Volume 17 (2010)

Number 5

The maximal entropy measure detects non-uniform hyperbolicity

Pages: 851 – 866

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n5.a5

Author

Juan Rivera-Letelier (Facultad de Matemáticas, P. Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile)

Abstract

We characterize two of the most studied non-uniform hyperbolicity conditions for rational maps, semi-hyperbolicity and the topological Collet-Eckmann condition, in terms of the maximal entropy measure. With the same tools we give an extension of the result of Carleson, Jones and Yoccoz that semi-hyperbolicity characterizes those polynomial maps whose basin of attraction of infinity is a John domain, to rational maps having a completely invariant attracting basin.

Full Text (PDF format)