The failure of Ruelle's property for entire functions

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 confo...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 384; p. 107723
Main Authors Mayer, Volker, Zdunik, Anna
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.06.2021
Elsevier
Subjects
Holomorphic dynamics
Mathematics
Meromorphic functions
Ruelle's property
secondary
Meromorphic functions
Holomorphic dynamics
Ruelle's property
primary
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.107723