TY - JOUR
T1 - Diffeomorphism cocycles over partially hyperbolic systems
AU - Sadovskaya, Victoria
N1 - Publisher Copyright:
© 2020 The Author(s). Published by Cambridge University Press.
PY - 2022/1/28
Y1 - 2022/1/28
N2 - We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold. We obtain several results for this setting. If a cocycle is bounded in, we show that it has a continuous invariant family of-Hölder Riemannian metrics on. We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.
AB - We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold. We obtain several results for this setting. If a cocycle is bounded in, we show that it has a continuous invariant family of-Hölder Riemannian metrics on. We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.
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U2 - 10.1017/etds.2020.131
DO - 10.1017/etds.2020.131
M3 - Article
AN - SCOPUS:85099125365
SN - 0143-3857
VL - 42
SP - 263
EP - 286
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 1
ER -