Ruelle operator and transcendental entire maps
Dynamical Systems
2016-08-16 v1 Complex Variables
Abstract
If is a transcendental entire function with only algebraic singularities we calculate the Ruelle operator of . Moreover, we prove both (i) if has a summable critical point, then is not structurally stable under certain topological conditions and (ii) if all critical points of belonging to Julia set are summable, then there exists no invariant lines fields in the Julia set.
Keywords
Cite
@article{arxiv.math/0201200,
title = {Ruelle operator and transcendental entire maps},
author = {P. Domínguez and P. Makienko and G. Sienra},
journal= {arXiv preprint arXiv:math/0201200},
year = {2016}
}