Wandering domains with nearly bounded orbits
Dynamical Systems
2023-08-01 v1 Complex Variables
Abstract
A major open question in transcendental dynamics asks if it is possible for points in a wandering domain to have bounded orbits, and more strongly, for a wandering domain to iterate only in a bounded domain. In this paper we give a partial answer to this question, by constructing a bounded wandering domain that spends, in a precise sense, nearly all of its time iterating in a bounded domain. This is in strong contrast to all previously known examples of wandering domains.
Keywords
Cite
@article{arxiv.2307.16682,
title = {Wandering domains with nearly bounded orbits},
author = {Leticia Pardo-Simón and David J. Sixsmith},
journal= {arXiv preprint arXiv:2307.16682},
year = {2023}
}
Comments
13 pages, 2 figures