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Diffeomorphism cocycles over partially hyperbolic systems
- Source :
- Ergodic Theory and Dynamical Systems. 42:263-286
- Publication Year :
- 2020
- Publisher :
- Cambridge University Press (CUP), 2020.
-
Abstract
- We consider H\"older continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma}$, we show that it has a continuous invariant family of $\gamma$-H\"older Riemannian metrics on $M$. We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ 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.<br />Comment: 24 pages
- Subjects :
- 010302 applied physics
Pure mathematics
Mathematics::Dynamical Systems
Mathematics::Operator Algebras
Fiber (mathematics)
Group (mathematics)
Applied Mathematics
General Mathematics
010102 general mathematics
Hölder condition
Dynamical Systems (math.DS)
01 natural sciences
Manifold
37D30, 37C15
Conjugacy class
Mathematics::K-Theory and Homology
Bounded function
0103 physical sciences
FOS: Mathematics
Mathematics::Differential Geometry
Diffeomorphism
Mathematics - Dynamical Systems
0101 mathematics
Invariant (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 14694417 and 01433857
- Volume :
- 42
- Database :
- OpenAIRE
- Journal :
- Ergodic Theory and Dynamical Systems
- Accession number :
- edsair.doi.dedup.....6b7e2e19dd62a63863a4dfd5ceee0b46