DCDS
Ruelle operator and transcendental entire maps
Patricia Domínguez Peter Makienko Guillermo Sienra
Discrete & Continuous Dynamical Systems - A 2005, 12(4): 773-789 doi: 10.3934/dcds.2005.12.773
We calculate the Ruelle operator of a transcendental entire function $f$ having only a finite set of algebraic singularities. Moreover, under certain topological conditions on the postcritical set we prove (i) if $f$ has a summable critical point, then $f$ is not structurally stable and (ii) if all critical points of $f$ belonging to Julia set are summable, then there do not exist invariant lines fields on the Julia set.
keywords: entire functions Ruelle operator Fatou set Julia set invariant line fields.

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