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Measure rigidity for some transcendental meromorphic functions

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


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