Rigidity of critical circle mappings, I

Details Rigidity of critical circle mappings, I Rigidity of critical circle mappings, I

1997-11-15

arxiv.org/abs/math/9711214v1

Mathematics

Dynamical Systems

Scientific paper

We prove that two $C^r$ critical circle maps with the same rotation number of bounded type are $C^{1+\alpha}$ conjugate for some $\alpha>0$ provided their successive renormalizations converge together at an exponential rate in the $C^0$ sense. The number $\alpha$ depends only on the rate of convergence. We also give examples of $C^\infty$ critical circle maps with the same rotation number that are not $C^{1+\beta}$ conjugate for any $\beta>0$.

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