# American Institute of Mathematical Sciences

July  2012, 32(7): 2375-2402. doi: 10.3934/dcds.2012.32.2375

## Measure rigidity for some transcendental meromorphic functions

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

Received  December 2009 Revised  July 2010 Published  March 2012

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.
Citation: Agnieszka Badeńska. Measure rigidity for some transcendental meromorphic functions. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2375-2402. doi: 10.3934/dcds.2012.32.2375
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