Generic H\"older foliations with smooth leaves

Enzo Fuentes

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arXiv · 1804.11016

Generic H\"older foliations with smooth leaves

Enzo Fuentes

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Abstract

In this work, we consider a specific space of foliations with $C^1$ leaves and H\"older 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.

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Enzo Fuentes. 2018-04-30. Generic H\"older foliations with smooth leaves. https://arxiv.org/abs/1804.11016

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