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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 conformal measure that is supported on the radial Julia set.

preprint2021arXivOpen access
Volker MayerAnna Zdunik
math.DS
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Volker MayerAnna Zdunik

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