Perturbations of exponential maps: Non-recurrent dynamics
Dynamical Systems
2024-10-10 v2
Abstract
We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones.
Cite
@article{arxiv.2206.11093,
title = {Perturbations of exponential maps: Non-recurrent dynamics},
author = {Magnus Aspenberg and Weiwei Cui},
journal= {arXiv preprint arXiv:2206.11093},
year = {2024}
}
Comments
Author accepted version. Overall revisions on Section 2 and simplified proofs for Lemmas 3.2 and 3.3; several references added. To appear in Journal d'Analyse Math\'ematique