Two conjectures on coarse conjugacy by Geller and Misiurewicz
Dynamical Systems
2025-03-04 v3 Group Theory
Metric Geometry
Abstract
In their study of coarse entropy, W. Geller and M. Misiurewicz introduced the notion of coarse conjugacy: a version of conjugacy appropriate for dynamics on metric spaces observed from afar. They made two conjectures on coarse conjugacy generalising their results. We disprove both of these conjectures. We investigate the impact of extra assumptions on the validity of the conjectures: We show that the result of Geller and Misiurewicz towards one of the conjectures can be considered optimal, and we prove the other conjecture under an assumption complementary to that from the referenced work.
Cite
@article{arxiv.2203.16953,
title = {Two conjectures on coarse conjugacy by Geller and Misiurewicz},
author = {Damian Sawicki},
journal= {arXiv preprint arXiv:2203.16953},
year = {2025}
}
Comments
Accepted in DCDS. Minor corrections in v2, cosmetic in v3. 13 pages