Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems

DOI10.1017/S014338570900039XzbMath1230.37042OpenAlexW2962915994MaRDI QIDQ3583784

Alistair Windsor, Rafael de la Llave

Publication date: 18 August 2010

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s014338570900039x

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

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Cites Work

• Unnamed Item
• Unnamed Item
• A regularity lemma for functions of several variables
• Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties
• Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
• Some inverse spectral results for negatively curved 2-manifolds
• Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
• The spectrum of positive elliptic operators and periodic bicharacteristics
• On Livšic's theorem, superrigidity, and Anosov actions of semisimple Lie groups
• Cocycles over abelian TNS actions
• A Banach algebra version of the Livsic theorem
• Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices
• Quasiconformality in the geodesic flow of negatively curved manifolds
• Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
• On uniformly quasiconformal Anosov systems
• Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
• Neighborhoods of hyperbolic sets
• Local Hölder regularity of densities and Livsic theorems for non-uniformly hyperbolic diffeomor\-phisms
• Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups
• Livsic theorems for connected Lie groups
• Remarks on Sobolev regularity in Anosov systems
• Livšic's theorem for semisimple Lie groups
• On Anosov diffeomorphisms with asymptotically conformal periodic data
• Regularity of solutions to the measurable Livsic equation
• Regularity of the transfer map for cohomologous cocycles
• The Livšic periodic point theorem for non-abelian cocycles
• Remarks on Livšic' theory for nonabelian cocycles
• Analytic conjugation of diffeomorphisms in ${\Bbb T}^{n}$}
• The Livsic Cocycle Equation for Compact Lie Group Extensions of Hyperbolic Systems
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• ON LOCAL AND GLOBAL RIGIDITY OF QUASI-CONFORMAL ANOSOV DIFFEOMORPHISMS
• Livšic theorems and stable ergodicity for group extensions of hyperbolic systems with discontinuities
• Livšic Regularity Theorems for Twisted Cocycle Equations Over Hyperbolic Systems
• Rigidity in Dynamics and Geometry
• Smooth cocycle rigidity for expanding maps, and an application to Mostow rigidity
• Livsic theorems for hyperbolic flows
• Periodic points and invariant pseudomeasures for toral endomorphisms
• Rigidity of higher-dimensional conformal Anosov systems
• Further rigidity properties of conformal Anosov systems
• Livšic regularity for Markov systems
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms