English

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 C1+αC^{1+\alpha} regularity, where α\alpha depends only on the bound on the type of the rotation number. We then extend this rigidity result to C3C^3-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}
}