Livšic theorem for matrix cocycles
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Publication:640761
DOI10.4007/annals.2011.173.2.11zbMath1238.37008arXiv0808.0350OpenAlexW2963242705MaRDI QIDQ640761
Publication date: 20 October 2011
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0808.0350
Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) General theory of random and stochastic dynamical systems (37H05)
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Cites Work
- Unnamed Item
- Unnamed Item
- Linear cocycles over hyperbolic systems and criteria of conformality
- Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
- Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
- Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
- On growth rates of subadditive functions for semiflows
- On Livšic's theorem, superrigidity, and Anosov actions of semisimple Lie groups
- Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices
- Global rigidity of certain Abelian actions by toral automorphisms
- Livsic theorems for connected Lie groups
- Livšic's theorem for semisimple Lie groups
- Lyapunov exponents of hyperbolic measures and hyperbolic periodic orbits
- Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems
- Regularity of the transfer map for cohomologous cocycles
- The Livšic periodic point theorem for non-abelian cocycles
- Remarks on Livšic' theory for nonabelian cocycles
- The Livsic Cocycle Equation for Compact Lie Group Extensions of Hyperbolic Systems
- Livšic Regularity Theorems for Twisted Cocycle Equations Over Hyperbolic Systems
- COHOMOLOGY OF DYNAMICAL SYSTEMS