Rigidity of critical circle maps
classification
🧮 math.DS
keywords
circlecriticalmapsnumberrotationsamealmostalpha
read the original 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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