The rigidity problem for analytic critical circle maps

D. Khmelev; M. Yampolsky

The rigidity problem for analytic critical circle maps

动力系统 2009-09-29 v2

作者: D. Khmelev , M. Yampolsky

摘要

It is shown that if $f$ and $g$ are any two analytic critical circle mappings with the same irrational rotation number, then the conjugacy that maps the critical point of $f$ to that of $g$ has regularity $C^{1+\alpha}$ at the critical point, with a universal value of $\alpha>0$ . As a consequence, a new proof of the hyperbolicity of the full renormalization horseshoe of critical circle maps is given.

关键词

thurston maps

引用

@article{arxiv.math/0501448,
  title  = {The rigidity problem for analytic critical circle maps},
  author = {D. Khmelev and M. Yampolsky},
  journal= {arXiv preprint arXiv:math/0501448},
  year   = {2009}
}

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