Publication: Absolute continuity, Lyapunov exponents, and rigidity II: systems with compact center leaves
Absolute continuity, Lyapunov exponents, and rigidity II: systems with compact center leaves
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Avila, A., Viana, M., & Wilkinson, A. (2022). Absolute continuity, Lyapunov exponents, and rigidity II: systems with compact center leaves. Ergodic Theory and Dynamical Systems, 42(2), 437–490. https://doi.org/10.1017/etds.2021.42
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We explore new connections between the dynamics of conservative partially hyperbolic systems and the geometric measure-theoretic properties of their invariant foliations. Our methods are applied to two main classes of volume-preserving diffeomorphisms: fibered partially hyperbolic diffeomorphisms and center-fixing partially hyperbolic systems. When the center is one-dimensional, assuming the diffeomorphism is accessible, we prove that the disintegration of the volume measure along the center foliation is either atomic or Lebesgue. Mor
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- Avila, Artur
- Viana, Marcelo
- Wilkinson, Amie
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Avila, A., Viana, M., & Wilkinson, A. (2022). Absolute continuity, Lyapunov exponents, and rigidity II: systems with compact center leaves. Ergodic Theory and Dynamical Systems, 42(2), 437–490. https://doi.org/10.1017/etds.2021.42
