TY - JOUR
T1 - ON REGULARITY OF CONJUGACY BETWEEN LINEAR COCYCLES OVER PARTIALLY HYPERBOLIC SYSTEMS
AU - Kalinin, Boris
AU - Sadovskaya, Victoria
N1 - Publisher Copyright:
© 2024 American Institute of Mathematical Sciences. All rights reserved.
PY - 2024/5
Y1 - 2024/5
N2 - 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.
AB - 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.
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U2 - 10.3934/dcds.2023145
DO - 10.3934/dcds.2023145
M3 - Article
AN - SCOPUS:85187711908
SN - 1078-0947
VL - 44
SP - 1287
EP - 1303
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 5
ER -