Leticia Pardo-Simón, David J. Sixsmith
Published 2023-07-31Version 1
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.
Comments: 13 pages, 2 figures
Bounded orbits of certain diagonalizable flows on $SL_{n}(\mathbb{R})/SL_{n}(\mathbb{Z})$
Bounded orbits and global fixed points for groups acting on the plane
Bounded orbits of diagonalizable flows on $\rm{SL}_3(\mathbb{R})/\rm{SL}_3(\mathbb{Z})$
![QR code for arXiv:2307.16682 [math.DS]](http://oss.arxitics.com/images/favicon.svg)