Livšic theorem for diffeomorphism cocycles

DOI10.1007/s00039-018-0454-yzbMath1420.37033arXiv1711.02135OpenAlexW2963167405MaRDI QIDQ2324613

Artur Avila, Alejandro Kocsard, Xiao-Chuan Liu

Publication date: 11 September 2019

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.02135

zbMATH Keywords

cocyclesLivšic theoremlocalization hypothesis

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) General theory of random and stochastic dynamical systems (37H05) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (9)

Relating boundary and interior solutions of the cohomological equation for cocycles by isometries of negatively curved spaces. The Lǐsic case* ⋮ Livšic theorems for Banach cocycles: existence and regularity ⋮ The Burnside problem for \(\text{Diff}_{\omega}(\mathbb{S}^2)\) ⋮ 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 ⋮ Cohomology of fiber-bunched twisted cocycles over hyperbolic systems ⋮ A Livšic theorem for matrix cocycles over non-uniformly hyperbolic systems ⋮ Livšic theorem for matrix cocycles over an axiom a flow

Cites Work

• Livšic theorem for low-dimensional diffeomorphism cocycles
• Smooth dependence on parameters of solutions to cohomology equations over Anosov systems with applications to cohomology equations on diffeomorphism groups
• Livšic theorem for matrix cocycles
• On the ergodicity of partially hyperbolic systems
• Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices
• Cocycles' stability for partially hyperbolic systems
• Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems
• A Livšic type theorem for germs of analytic diffeomorphisms
• The cohomological equation for partially hyperbolic diffeomorphisms
• Invariant manifolds
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