Rotation sets for random compositions of $\T$ homeomorphisms
Dynamical Systems
2025-10-15 v1
Abstract
We study cocycles of homeomorphisms of in the isotopy class of the identity over shift spaces, using as a tool a novel definition of rotation sets inspired in the classical work of Miziurewicz and Zieman. We discuss different notions of rotation sets, for the full cocyle as well as for measures invariant by the shift dynamics on the base. We present some initial results on the shape of rotation sets, continuity of rotation sets for shift-invariant measures, and bounded displacements for irrotational cocyles, as well as a few interesting examples in an attempt to motive the development of the topic.
Cite
@article{arxiv.2510.11989,
title = {Rotation sets for random compositions of $\T$ homeomorphisms},
author = {Catalina Freijo and Fabio Tal},
journal= {arXiv preprint arXiv:2510.11989},
year = {2025}
}