Measure rigidity for some transcendental meromorphic functions

Agnieszka Badeńska

doi:10.3934/dcds.2012.32.2375

Article Contents

2012, Volume 32, Issue 7: 2375-2402. Doi: 10.3934/dcds.2012.32.2375

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Measure rigidity for some transcendental meromorphic functions

Agnieszka Badeńska^1,

1.
Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa

Received: December 2009

Revised: July 2010

Published: July 2012

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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.

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Mathematics Subject Classification: Primary: 37F10; Secondary: 30D05.

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