Singular values and non-repelling cycles for entire transcendental maps
Dynamical Systems
2017-12-04 v1
Abstract
Let be a map with bounded set of singular values for which periodic dynamic rays exist and land. We prove that each non-repelling cycle is associated to a singular orbit which cannot accumulate on any other non-repelling cycle. When has finitely many singular values this implies a refinement of the Fatou-Shishikura inequality. Our approach is combinatorial in the spirit of the approach used by [Ki00], [BCL+16] for polynomials.
Keywords
Cite
@article{arxiv.1712.00273,
title = {Singular values and non-repelling cycles for entire transcendental maps},
author = {Anna Miriam Benini and Núria Fagella},
journal= {arXiv preprint arXiv:1712.00273},
year = {2017}
}
Comments
13 pages, 1 figure