Center foliation: absolute continuity, disintegration and rigidity

DOI10.1017/etds.2014.53zbMath1365.37034arXiv1302.1637OpenAlexW3099757505MaRDI QIDQ2793108

Régis Varão

Publication date: 15 March 2016

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

Full work available at URL: https://arxiv.org/abs/1302.1637

zbMATH Keywords

rigiditypartially hyperbolic diffeomorphismcenter foliation

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) Invariant manifold theory for dynamical systems (37D10) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (15)

Synchronization properties of random piecewise isometries ⋮ New derived from Anosov diffeomorphisms with pathological center foliation ⋮ Anosov endomorphisms on the two-torus: regularity of foliations and rigidity ⋮ Disintegrations of non‐hyperbolic ergodic measures along the center foliation of DA maps ⋮ Conditions for atomic disintegration to be monoatomic ⋮ A note on rigidity of Anosov diffeomorphisms of the three torus ⋮ Minimal yet measurable foliations ⋮ Measure-theoretical properties of center foliations ⋮ Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems ⋮ Geometric growth for Anosov maps on the 3 torus ⋮ Pathological center foliation with dimension greater than one ⋮ Rigidity for partially hyperbolic diffeomorphisms ⋮ Uniqueness and continuity of equilibrium states for DA-diffeomorphisms ⋮ Lyapunov exponents and smooth invariant foliations for partially hyperbolic diffeomorphisms on ⋮ Center Lyapunov exponents in partially hyperbolic dynamics

Cites Work

• \(C^1\)-differentiable conjugacy of Anosov diffeomorphisms on three dimensional torus
• Geometric expansion, Lyapunov exponents and foliations
• How typical are pathological foliations in partially hyperbolic dynamics: an example
• Transitive partially hyperbolic diffeomorphisms on 3-manifolds
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Dynamical coherence of partially hyperbolic diffeomorphisms of the 3-torus
• Removing zero Lyapunov exponents
• Leaf conjugacies on the torus
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Absolutely singular dynamical foliations

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