Integrability of dominated decompositions on three-dimensional manifolds

TL;DR

This paper studies the conditions under which certain invariant distributions in 3-manifolds are integrable, proving unique integrability for various classes of dominated decompositions with specific regularity.

Contribution

It establishes the unique integrability of Lipschitz continuous invariant decompositions under dynamical domination and volume domination conditions in 3-manifolds.

Findings

Unique integrability of Lipschitz invariant distributions under domination conditions

Integrability results extend to distributions with certain regularity properties

Provides new insights into the structure of invariant decompositions in dynamical systems

Abstract

We investigate the integrability of 2-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular we prove unique integrability of dynamically dominated and volume dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.