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Ruelle operator and transcendental entire maps

P. Domínguez·P. Makienko·G. Sienra
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Abstract

If $f$ is a transcendental entire function with only algebraic singularities we calculate the Ruelle operator of $f$. Moreover, we prove both (i) if $f$ has a summable critical point, then $f$ is not structurally stable under certain topological conditions and (ii) if all critical points of $f$ belonging to Julia set are summable, then there exists no invariant lines fields in the Julia set.

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P. Domínguez, P. Makienko, G. Sienra. 2002-01-21. Ruelle operator and transcendental entire maps. https://arxiv.org/abs/math/0201200

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