Minimality and stable Bernouliness in dimension 3

TL;DR

This paper demonstrates that in 3-dimensional manifolds, the presence of a minimal expanding invariant foliation generically leads to stable Bernoulliness, linking geometric structures to statistical properties.

Contribution

It establishes a generic link between minimal expanding foliations and stable Bernoulliness in 3D manifolds, a novel result in dynamical systems.

Findings

Minimal expanding invariant foliations imply stable Bernoulliness

The result holds generically in $Diff^1_m(M)$ for 3D manifolds

Connects geometric foliation properties with statistical stability

Abstract

In 3-dimensional manifolds, we prove that generically in$Diff^1_m(M)$, the existence of a minimal expanding invariant foliation implies stable Bernoulliness.