Measure rigidity for some transcendental meromorphic functions

Pages: 2375 - 2402, Volume 32, Issue 7, July 2012

doi:10.3934/dcds.2012.32.2375       Abstract        References        Full Text (501.6K)       Related Articles

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

Received: December 2009;      Revised: July 2010;      Published: March 2012.

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