Artículos de revistas
Minimal yet measurable foliations
Fecha
2014-03Registro en:
Journal of Modern Dynamics, Springfield, v.8, n.1, p.93-107, 2014
1930-5311
10.3934/jmd.2014.8.93
Autor
Ponce, Gabriel
Tahzibi, Ali
Varão, Régis
Institución
Resumen
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.