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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Center foliation: absolute continuity, disintegration and rigidity

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Varao, Regis
Total Authors: 1
Document type: Journal article
Source: Ergodic Theory and Dynamical Systems; v. 36, n. 1, p. 256-275, FEB 2016.
Web of Science Citations: 7

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)

FAPESP's process: 12/06553-9 - Partially hyperbolic diffeomorphisms: absolute continuity, rigidity, Lyapunov exponents
Grantee:José Régis Azevedo Varão Filho
Support type: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 11/21214-3 - Absolute continuity of the central foliation for partially hyperbolic systems
Grantee:José Régis Azevedo Varão Filho
Support type: Scholarships in Brazil - Post-Doctorate