English

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