Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices

DOI10.1215/S0012-7094-95-07920-4zbMath0849.58049OpenAlexW1525499438MaRDI QIDQ1913358

Andrei Török, Viorel Niţiča

Publication date: 10 June 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-95-07920-4

zbMATH Keywords

structural stabilityAnosov actionscohomology of dynamical systemsdeformation rigidity

Mathematics Subject Classification ID

Dynamical systems with hyperbolic behavior (37D99)

Related Items (21)

Fiber bunching and cohomology for Banach cocycles over hyperbolic systems ⋮ Livšic theorem for low-dimensional diffeomorphism cocycles ⋮ Rigidity of higher rank Abelian cocycles with values in diffeomorphism groups ⋮ Local rigidity of affine actions of higher rank groups and lattices ⋮ Boundedness, compactness, and invariant norms for Banach cocycles over hyperbolic systems ⋮ Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus ⋮ On local rigidity of partially hyperbolic affine \(\mathbb{Z}^k\) actions ⋮ Noncommutative coboundary equations over integrable systems ⋮ Livšic theorem for matrix cocycles ⋮ Anatole Katok ⋮ Certain new robust properties of invariant sets and attractors of dynamical systems ⋮ Attractors and skew products ⋮ Livšic theorem for Banach rings ⋮ Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems ⋮ Cohomology of fiber bunched cocycles over hyperbolic systems ⋮ Boundedness and invariant metrics for diffeomorphism cocycles over hyperbolic systems ⋮ Diffeomorphism group valued cocycles over higher-rank abelian Anosov actions ⋮ Diffeomorphism cocycles over partially hyperbolic systems ⋮ Livšic theorem for diffeomorphism cocycles ⋮ A Livšic theorem for matrix cocycles over non-uniformly hyperbolic systems ⋮ Existence and uniqueness for directional attractors of topological cocycles

Cites Work

• Infinitesimal regidity for smooth actions of discrete subgroups of Lie groups
• 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
• On a regularity problem occurring in connection with Anosov diffeomorphisms
• On the cohomology of certain dynamical systems
• Rigidity for Anosov actions of higher rank lattices
• Local rigidity for certain groups of toral automorphisms
• Infinitesimal rigidity for hyperbolic actions
• Topological deformation rigidity of higher rank lattice actions
• Cocycle superrigidity and rigidity for lattice actions on tori
• Global rigidity results for lattice actions on tori and new examples of volume-preserving actions
• Cartan subgroups and lattices in semi-simple groups
• Stable Orbits of Differentiable Group Actions
• Dynamical systems with hyperbolic structure
• The Stationary Set of a Group Action
• Analytic regularity of solutions of Livsic's cohomology equation and some applications to analytic conjugacy of hyperbolic dynamical systems
• Higher cohomology for Abelian groups of toral automorphisms
• Invariant manifolds
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