Measure rigidity for some transcendental meromorphic functions
Agnieszka Badeńska - Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland (email)
Abstract: We consider hyperbolic meromorphic functions of the following form $f(z)=R\circ\exp(z)$, where $R$ is a non-constant rational function, satisfying so-called rapid derivative growth condition. We study several types of conjugacies in this class and prove a~measure rigidity theorem in the case when $f$ has a logarithmic tract over $\infty$ and under some additional assumptions.
Keywords: Holomorphic dynamics, hyperbolic function, thermodynamical
formalism, conformal measure, conjugacy, rigidity.
Received: December 2009; Revised: July 2010; Published: March 2012.
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