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Fine ergodic properties of partially hyperbolic dynamical systems

Ponce, Gabriel

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Título:
Fine ergodic properties of partially hyperbolic dynamical systems
Autor: Ponce, Gabriel
Orientador: Tahzibi, Ali
Assuntos: Desintegração De Medidas; Difeomorfismo Parcialmente Hiperbólicos; Folheações; Sistemas Dinâmicos; Teoria Ergódica
Descrição: Let f : T3 → T3 be a C2 volume preserving partially hyperbolic diffeomorphism homotopic to a linear Anosov automorphism A : T3 → T3. We prove that if f is Kolmogorov, then f is Bernoulli. We study the characteristics of atomic disintegration of the volume measure whenever it occurs. We prove that if the volume measure m has atomic disintegration on the center leaves then the disintegration has one atom per center leaf. We give a condition, depending only on the center Lyapunov exponent of the diffeomorphism, that guarantees atomic disintegration of the volume measure on center leaves. We construct an open family of diffeomorphisms satisfying this condition which generates the first examples of foliations which are both measurable and minimal. In this same construction we give the first examples of partially hyperbolic diffeomorphisms with zero center Lyapunov exponent and homotopic to a linear Anosov.
DOI: 10.11606/T.55.2014.tde-20032015-113539
Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Ciências Matemáticas e de Computação
Data de criação/publicação: 2014-11-21
Formato: Adobe PDF
Idioma: Inglês

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