Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers
Dynamical Systems
2021-12-14 v1
Abstract
We prove that if two analytic multicritical circle maps with the same bounded type rotation number are topologically conjugate by a conjugacy which matches the critical points of the two maps while preserving the orders of their criticalities, then the conjugacy necessarily has regularity, where depends only on the bound on the type of the rotation number. We then extend this rigidity result to -smooth bi-cubic circle maps.
Keywords
Cite
@article{arxiv.2112.05845,
title = {Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers},
author = {Igors Gorbovickis and Michael Yampolsky},
journal= {arXiv preprint arXiv:2112.05845},
year = {2021}
}