Livsic theorems for hyperbolic flows

DOI10.1090/S0002-9947-99-02428-9zbMath0995.37016OpenAlexW1496810181WikidataQ126003422 ScholiaQ126003422MaRDI QIDQ4699637

C. P. Walkden

Publication date: 17 November 1999

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02428-9

zbMATH Keywords

Lie groupsmeasurable solutionshyperbolic flowHölder continuousHölder cocycle equationsLivšic's results

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Lie groups (22E99) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

Related Items

Smooth Livšic regularity for piecewise expanding maps, Livsic theorems for connected Lie groups, Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems, Livšic measurable rigidity for 𝒞¹ generic volume-preserving Anosov systems, Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps, Livšic theorem for matrix cocycles over an axiom a flow

Cites Work

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• 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
• Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems
• The ergodic theory of axiom A flows
• Stable ergodicity of skew products of one-dimensional hyperbolic flows
• Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
• Markov partitions for Anosov flows on \(n\)-dimensional manifolds
• Regularity of the transfer map for cohomologous cocycles
• Measurable Cocycle Rigidity for Some Non-Compact Groups
• Analytic regularity of solutions of Livsic's cohomology equation and some applications to analytic conjugacy of hyperbolic dynamical systems
• Livšic Regularity Theorems for Twisted Cocycle Equations Over Hyperbolic Systems
• Symbolic Dynamics for Hyperbolic Flows