ON REGULARITY OF CONJUGACY BETWEEN LINEAR COCYCLES OVER PARTIALLY HYPERBOLIC SYSTEMS

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Abstract

We consider Hölder continuous GL(d, 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 any constant GL(d, 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 subbundles, Riemannian metrics, and conformal structures.

Original languageEnglish (US)
Pages (from-to)1287-1303
Number of pages17
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume44
Issue number5
DOIs
StatePublished - May 2024

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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