The failure of Ruelle's property for entire functions
Dynamical Systems
2021-01-06 v3
Abstract
We exhibit an analytic family of hyperbolic, even disjoint type, entire functions for which the hyperbolic dimension does not vary analytically. Additionally we answer several questions in thermodynamic formalism of entire functions such as the existence of a hyperbolic entire function without conformal measure that is supported on the radial Julia set.
Keywords
Cite
@article{arxiv.1902.03753,
title = {The failure of Ruelle's property for entire functions},
author = {Volker Mayer and Anna Zdunik},
journal= {arXiv preprint arXiv:1902.03753},
year = {2021}
}
Comments
38 pages