Center-unstable foliations do not have compact leaves
Federico Rodriguez Hertz, Jana Rodriguez Hertz, Raul Ures

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.
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