Dominated splitting from constant periodic data and global rigidity of Anosov automorphisms

2023/09/13 by Jonathan DeWitt, DeWitt, Jonathan, Andrey Gogolev +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2309.07323

openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a GL(d,ℝ) cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov automorphisms of \mathbbT^d. Further, our approach also works when the periodic data is narrow, that is, sufficiently close to constant. We can show global periodic data rigidity for certain non-linear Anosov diffeomorphisms in a neighborhood of an irreducible Anosov automorphism with simple spectrum.

Cited by

• Dominated splittings and periodic data for quasi-compact operator cocycles

Related

• On Anosov diffeomorphisms with asymptotically conformal periodic data
• Smooth rigidity for very non-algebraic Anosov diffeomorphisms of codimension one
• Constant periodic data and rigidity
• Rigidity of Lyapunov exponents for derived from Anosov diffeomorphisms
• Joint integrability and spectral rigidity for Anosov diffeomorphisms