The failure of Ruelle's property for entire functions

2019/02/11 by Volker Mayer, Mayer, Volker, Anna Zdunik +1
Mathematics · #30D05 #37F45 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F10 #Secondary 28A78 #math.DS #msc:28A78 #msc:30D05 #msc:37F10 #msc:37F45

paper · pdf · doi:10.48550/arxiv.1902.03753

38 pages

arxiv created 2021/01/05 · arxiv updated 2021/01/06

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.

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