arXiv:2203.16953 Abstract | arXiv Analytics

arXiv:2203.16953 [math.DS]Abstract References Reviews Resources

Two conjectures on coarse conjugacy by Geller and Misiurewicz

Published 2022-03-31Version 1

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.

Comments: 13 pages

Categories: math.DS, math.GR, math.MG

Subjects: 37B02, 51F30

Keywords: conjecture, misiurewicz, assumption complementary, coarse entropy, extra assumptions

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