Generic Hölder foliations with smooth leaves

2018/04/30 by Fuentes, Enzo
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.11016

Abstract

In this work, we consider a specific space of foliations with C¹ leaves and Hölder holonomies of the square M=[0,1]², with some topology and we show that a generic such foliation is non-absolutely continuous, furthermore, the conditional measures defined by Rokhlin disintegration are Dirac measures on the leaves. This space of foliations is motivated by the foliations that appear in hyperbolic systems and partially hyperbolic systems.

Related

• Hölder foliations, revisited
• Dynamics and the Godbillon-Vey Class of C¹ Foliations
• Measure-theoretical properties of center foliations
• Topological description of Riemannian foliations with dense leaves
• Riemannian foliations and quasifolds