preprint-author: 
P. Guarino, M. Martens, and W. de Melo
preprint-title: 
Rigidity of critical circle maps
preprint-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.

preprint-year: 
2015