Livšic measurable rigidity for 𝒞¹ generic volume-preserving Anosov systems

DOI10.1090/proc12762zbMath1354.37028arXiv1410.8631OpenAlexW1499270960MaRDI QIDQ2790188

Yun Yang

Publication date: 3 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.8631

zbMATH Keywords

Anosov flowscentral limit theoremLivšic measurable rigidity

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Dynamical aspects of measure-preserving transformations (37A05) Rigidity results (53C24) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Cites Work

• On the regularization of conservative maps
• Livšic theorem for matrix cocycles
• Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
• The central limit theorem for geodesic flows on \(n\)-dimensional manifolds of negative curvature
• Cocycles' stability for partially hyperbolic systems
• Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms
• Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems
• The Livsic Cocycle Equation for Compact Lie Group Extensions of Hyperbolic Systems
• Livsic theorems for hyperbolic flows
• A pasting lemma and some applications for conservative systems
• The cohomological equation for partially hyperbolic diffeomorphisms
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• A generic \(C^1\) expanding map has a singular S-R-B measure
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