Minimality of one invariant lamination for partially hyperbolic attractors

TL;DR

This paper proves that for certain partially hyperbolic attractors with a one-dimensional center, at least one invariant lamination is minimal, extending previous results on minimal foliations in dynamical systems.

Contribution

It establishes the minimality of at least one invariant lamination in strongly partially hyperbolic attractors with a one-dimensional center, generalizing prior work on robustly transitive systems.

Findings

At least one invariant lamination is minimal in the specified attractors.

Extends minimal foliation results to a broader class of partially hyperbolic systems.

Provides a deeper understanding of the structure of invariant laminations in dynamical systems.

Abstract

We prove that at least one of the two invariant laminations of a strongly partially hyperbolic attractor with one-dimensional center bundle is minimal. This result extends those in [7] about minimal foliations for robustly transitive diffeomorphisms.