2023/09/17 by Boris Kalinin, Victoria Sadovskaya, Kalinin, Boris +1
Mathematics · Physics and Astronomy · #37C15 #37D20 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2309.09130
openalex publication_date 2023/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Hölder continuous GL(d,\mathbb R)-valued cocycles, and more generally linear cocycles, over an accessible volume-preserving center-bunched partially hyperbolic diffeomorphism. We study the regularity of a conjugacy between two cocycles. We establish continuity of a measurable conjugacy between \em any constant GL(d,\mathbb R)-valued cocycle and its perturbation. We deduce this from our main technical result on continuity of a measurable conjugacy between a fiber bunched linear cocycle and a cocycle with a certain block-triangular structure. The latter class covers constant cocycles with one Lyapunov exponent. We also establish a result of independent interest on continuity of measurable solutions for twisted vector-valued cohomological equations over partially hyperbolic systems. In addition, we give more general versions of earlier results on regularity of invariant subbudles, Riemannian metrics, and conformal structures.