Cohomology of dominated diffeomorphism-valued cocycles over hyperbolic systems
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Publication:2827493
DOI10.1017/etds.2014.149zbMath1378.37006arXiv1408.3085OpenAlexW3101301275MaRDI QIDQ2827493
Alejandro Kocsard, Lucas H. Backes
Publication date: 20 October 2016
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1408.3085
Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Partially hyperbolic systems and dominated splittings (37D30) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)
Related Items (10)
Fiber bunching and cohomology for Banach cocycles over hyperbolic systems ⋮ Livšic theorem for low-dimensional diffeomorphism cocycles ⋮ Rigidity of fiber bunched cocycles ⋮ On the periodic approximation of Lyapunov exponents for semi-invertible cocycles ⋮ Periodic approximation of Oseledets subspaces for semi-invertible cocycles ⋮ Simple Lyapunov spectrum for certain linear cocycles over partially hyperbolic maps ⋮ Boundedness and invariant metrics for diffeomorphism cocycles over hyperbolic systems ⋮ Diffeomorphism cocycles over partially hyperbolic systems ⋮ Cohomology of fiber-bunched twisted cocycles over hyperbolic systems ⋮ A Livšic theorem for matrix cocycles over non-uniformly hyperbolic systems
Cites Work
- On cohomological \(C^0\)-(in)stability
- Livšic theorem for matrix cocycles
- A regularity lemma for functions of several variables
- Extremal Lyapunov exponents: an invariance principle and applications
- Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
- Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents
- Livšic's theorem for semisimple Lie groups
- Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems
- The Livšic periodic point theorem for non-abelian cocycles
- Remarks on Livšic' theory for nonabelian cocycles
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