Absolutely singular dynamical foliations

Abstract

We show that for the C^1-open set of partially hyperbolic diffeomorphisms constructed in (M. Shub and A. Wilkinson, "Pathological foliations and removable zero exponents," Invent. math. 139 (2000) 3, 495-508), Lebesgue measure on the 3-torus decomposes as atomic measure along the leaves of the central foliation.

9 pages. See also http://www.math.nwu.edu/~wilkinso

Cited by in corpus (29)

• Response solutions for arbitrary quasi-periodic perturbations with Bryuno frequency vector
• Non-hyperbolic ergodic measures with large support
• A survey on partially hyperbolic dynamics
• Center foliation: absolute continuity, disintegration and rigidity
• Nonequilibrium and Fluctuation Relation
• Measure theory through dynamical eyes
• Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems
• Lyapunov exponents and rigidity of Anosov automorphisms and skew products
• Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms
• Resonances within Chaos
• Maximizing measures for partially hyperbolic systems with compact center leaves
• Mono-atomic disintegration and Lyapunov exponents for derived from Anosov diffeomorphisms
• Physical Measure and Absolute Continuity for One-Dimensional Center Direction
• Existence of physical measures in some Excitation-Inhibition Networks
• Center Lyapunov exponents in partially hyperbolic dynamics
• Circle diffeomorphisms forced by expanding circle maps
• Synchronization properties of random piecewise isometries
• Disintegrations of non-hyperbolic ergodic measures along the center foliation of DA maps
• Regularity of Lyapunov Exponents for Diffeomorphisms with Dominated Splitting
• Holder properties of perturbed skew products and Fubini regained
• Atomic disintegrations for partially hyperbolic diffeomorphisms
• Nonhyperbolic step skew-products: Ergodic approximation
• Uniform hyperbolicity for random maps with positive Lyapunov exponents
• New Derived from Anosov Diffeomorphisms with pathological center foliation
• Pathological center foliation with dimension greater than one
• The disintegration of measures with periodic repetitive pattern
• Classification of Conditional Measures Along Certain Invariant One-Dimensional Foliations
• Generic Hölder foliations with smooth leaves
• Lyapunov exponents and regularity of invariant foliations for partially hyperbolic diffeomophisms on ${\mathbb{T}}^3$