Rigidity of critical circle maps

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.

46 pages, 5 figures

References in corpus (1)

• Real bounds and Lyapunov exponents

Cited by in corpus (14)

• Beau bounds for multicritical circle maps
• The Rigidity Conjecture
• Renormalization of bicritical circle maps
• Instability of Renormalization
• Complex a priori bounds for multicritical circle maps with bounded type rotation number
• Automorphic measures and invariant distributions for circle dynamics
• Invariant Manifolds for Non-differentiable Operators
• Dynamics of asymptotically holomorphic polynomial-like maps
• The boundary of chaos for interval mappings
• The thermodynamic formalism and central limit theorem for stochastic perturbations of circle maps with a break
• Dynamics of multicritical circle maps
• Quasisymmetric orbit-flexibility of multicritical circle maps
• On the Hausdorff dimension of invariant measures for multicritical circle maps
• Rigidity for circle diffeomorphisms with breaks satisfying a Zygmund smoothness condition