Year: 2011
Type: article
Abstract: Letfbe an arbitrary transcendental entire or meromorphic function in the class 𝒮 (i.e. with finitely many singularities). We show that the topological pressureP(f,t) fort>0 can be defined as the common value of the pressuresP(f,t,z) for allz∈ℂ up to a set of Hausdorff dimension zero. Moreover, we prove thatP(f,t) equals the supremum of the pressures off∣Xover all invariant hyperbolic subsetsXof the Julia set, and we prove Bowen’s formula forf, i.e. we show that the Hausdorff dimension of the radial Julia set offis equal to the infimum of the set oft, for whichP(f,t) is non-positive. Similar results hold for (non-exceptional) transcendental entire or meromorphic functionsfin the class ℬ (i.e. with a bounded set of singularities), for which the closure of the post-singular set does not contain the Julia set.
Authors: KRZYSZTOF BARAŃSKI, BOGUSŁAWA KARPIŃSKA, ANNA ZDUNIK
Institutions: University of Warsaw, Warsaw University of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2060988241