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arXiv · 1902.03753

The failure of Ruelle's property for entire functions

Volker Mayer·Anna Zdunik
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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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Volker Mayer, Anna Zdunik. 2019-02-11. The failure of Ruelle's property for entire functions. https://arxiv.org/abs/1902.03753

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