Center-unstable foliations do not have compact leaves

TL;DR

This paper proves that for certain 3-manifold systems, invariant foliations tangent to the center-unstable or center-stable bundles cannot contain compact leaves, revealing a fundamental property of their structure.

Contribution

It establishes a new result showing the non-existence of compact leaves in invariant foliations tangent to center-unstable or center-stable bundles in partially hyperbolic 3-manifold diffeomorphisms.

Findings

Invariant foliations tangent to center-unstable bundles have no compact leaves.

The result applies to all partially hyperbolic diffeomorphisms on 3-manifolds.

Provides insight into the structure of invariant foliations in dynamical systems.

Abstract

For a partiallyhyperbolic diffeomorphism on a 3-manifold, we show that any invariant foliation tangent to the center-unstable (or center-stable) bundle has no compact leaves.