Infinite-dimensional Thurston theory and transcendental dynamics II: classification of entire functions with escaping singular orbits
Dynamical Systems
2025-07-29 v5
Abstract
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional Teichm\"uller space, analogously to the Thurston's classical Topological Characterization of Rational Functions, but for an infinite set of marked points.
Keywords
Cite
@article{arxiv.2102.10728,
title = {Infinite-dimensional Thurston theory and transcendental dynamics II: classification of entire functions with escaping singular orbits},
author = {Konstantin Bogdanov},
journal= {arXiv preprint arXiv:2102.10728},
year = {2025}
}
Comments
26 pages, 0 figures, accepted manuscript: minor improvements throughout the article, some proofs slightly upgraded. This article draws heavily from arXiv:2102.00300