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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.)

MINIMAL YET MEASURABLE FOLIATIONS

Full text
Author(s):
Ponce, Gabriel [1] ; Tahzibi, Ali [1] ; Varao, Regis [1]
Total Authors: 3
Affiliation:
[1] ICMC USP, Dept Matemat, Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: JOURNAL OF MODERN DYNAMICS; v. 8, n. 1, p. 93-107, MAR 2014.
Web of Science Citations: 8
Abstract

In this paper we mainly address the problem of disintegration of Lebesgue measure along the central foliation of volume-preserving diffeomorphisms isotopic to hyperbolic automorphisms of 3-torus. We prove that atomic disintegration of the Lebesgue measure (ergodic case) along the central foliation has the peculiarity of being mono-atomic (one atom per leaf). This implies the measurability of the central foliation. As a corollary we provide open and nonempty subset of partially hyperbolic diffeomorphisms with minimal yet measurable central foliation. (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: 12/14620-8 - Fine ergodic properties of partially hyperbolic dynamical systems
Grantee:Gabriel Ponce
Support type: Scholarships abroad - Research Internship - Doctorate (Direct)
FAPESP's process: 09/16792-8 - Fine ergodic properties of partially hyperbolic systems
Grantee:Gabriel Ponce
Support type: Scholarships in Brazil - Doctorate (Direct)
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