Center foliation: absolute continuity, disintegration and rigidity

Autor(es)

Varao, Regis

• Tipo de documento: Artigo Científico
• Fonte: Ergodic Theory and Dynamical Systems; v. 36, p. 20-pg., 2016-02-01.

Resumo

In this paper we address the issues of absolute continuity for the center foliation, as well as the disintegration on the non-absolute continuous case and rigidity of volume-preserving partially hyperbolic diffeomorphisms isotopic to a linear Anosov automorphism on T-3. It is shown that the disintegration of volume on center leaves for these diffeomorphisms may be neither atomic nor Lebesgue, in contrast to the dichotomy (Lebesgue or atomic) obtained by Avila, Viana and Wilkinson [Absolute continuity, Lyapunov exponents and rigidity I: Geodesic flows. Preprint, 2012, arXiv:1110.2365v2] for perturbations of time-one of geodesic flow. In the case of atomic disintegration of volume on the center leaves of an Anosov diffeomorphism on T-3, we show that it has to be one atom per leaf. Moreover, we show that not even a C-1 center foliation implies a rigidity result. However, for a volume-preserving partially hyperbolic diffeomorphism isotopic to a linear Anosov automorphism, assuming the center foliation is C-1 and transversely absolutely continuous with bounded Jacobians, we obtain smooth conjugacy to its linearization. (AU)

• Processo FAPESP: 11/21214-3 - Continuidade absoluta da folheação central para sistemas parcialmente hiperbólico
• Beneficiário: José Régis Azevedo Varão Filho
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 12/06553-9 - Difeomorfismos parcialmente hiperbólicos: continuidade absoluta, rigidez, expoente de Lyapunov
• Beneficiário: José Régis Azevedo Varão Filho
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado