Ergodic exponential maps with escaping singular behaviours
Dynamical Systems
2026-04-08 v2 Complex Variables
Abstract
We construct exponential maps for which the singular value tends to infinity under iterates while the maps are ergodic. This is in contrast with a result of Lyubich from 1987 which tells that is not ergodic.
Cite
@article{arxiv.2308.10565,
title = {Ergodic exponential maps with escaping singular behaviours},
author = {Weiwei Cui and Jun Wang},
journal= {arXiv preprint arXiv:2308.10565},
year = {2026}
}
Comments
9 pages, 1 figure; Theorem 1.2 rephrased and the proof of the main Theorem 1 is reorganized. Author accepted version. To appear in Bulletin of the London Mathematical Society