Generic Hölder foliations with smooth leaves
In this work, we consider a specific space of foliations with $C^1$ 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.
math.DS↗