Higher cohomology for Abelian groups of toral automorphisms

DOI10.1017/S0143385700008531zbMath0851.57039MaRDI QIDQ4837583

Svetlana Katok, Anatole Katok

Publication date: 24 November 1996

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

zbMATH Keywords

torusautomorphismsFourier coefficientshyperbolic actionAnosov action

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Fourier series and coefficients in several variables (42B05) Dynamical systems with hyperbolic behavior (37D99)

Related Items

Higher cohomology of parabolic actions on certain homogeneous spaces ⋮ Limit theorems for higher rank actions on Heisenberg nilmanifolds ⋮ Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices ⋮ Degree two ergodic theorem for divergence-free stationary random fields ⋮ The first cohomology group, mixing and minimal sets of the commutative group of algebraic actions on a torus ⋮ On low discrepancy sequences and low discrepancy ergodic transformations of the multidimensional unit cube ⋮ Higher cohomology for Anosov actions on certain homogeneous spaces ⋮ Local rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torus ⋮ A central limit theorem for time-dependent dynamical systems ⋮ Equidistribution for higher-rank abelian actions on Heisenberg nilmanifolds ⋮ Invariant distributions and cohomology for geodesic flows and higher cohomology of higher-rank Anosov actions ⋮ Anatole Katok ⋮ Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks ⋮ Local rigidity of actions of higher rank abelian groups and KAM method ⋮ Rigidity of the Weyl chamber flow, and vanishing theorems of Matsushima and Weil

Cites Work

• Closed geodesics, periods and arithmetic of modular forms
• 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
• First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
• Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions
• Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
• Homology properties of Y-systems
• Deux théorèmes d'arithmétique