Global smooth rigidity for toral automorphisms
Abstract
Abstract We study regularity of a conjugacy between a hyperbolic or partially hyperbolic toral automorphism $L$ L and a $C^{\infty }$ C ∞ diffeomorphism $f$ f of the torus. For a very weakly irreducible hyperbolic automorphism $L$ L we show that any $C^{1}$ C 1 conjugacy is $C^{\infty }$ C ∞ . For a very weakly irreducible ergodic partially hyperbolic automorphism $L$ L we show that any $C^{1+\text{H\"{o}lder}}$ C 1 + Hölder conjugacy is $C^{\infty }$ C ∞ . As a corollary, we improve regularity of the conjugacy to $C^{\infty }$ C ∞ in prior local and global rigidity results.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Inventiones mathematicae
- Publisher
- Springer Science and Business Media LLC
- Volume
- 245
- Issue
- 3
- Pages
- 1139–1167
- Publication date
- 13 May 2026
- Language
- EN