Rigidity of critical circle maps

Published 9 Nov 2015 in math.DS | (1511.02792v1)

Abstract: We prove that any two $C^4$ critical circle maps with the same irrational rotation number and the same odd criticality are conjugate to each other by a $C^1$ circle diffeomorphism. The conjugacy is $C^{1+\alpha}$ for Lebesgue almost every rotation number.

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