Dynamical coherence of partially hyperbolic diffeomorphisms on nilmanifolds isotopic to Anosov

TL;DR

This paper establishes the dynamical coherence of certain partially hyperbolic diffeomorphisms on nilmanifolds, extending known results from tori to a broader class of manifolds, thus advancing understanding of their dynamical structure.

Contribution

It extends the dynamical coherence results for partially hyperbolic diffeomorphisms from tori to nilmanifolds isotopic to Anosov diffeomorphisms.

Findings

Dynamical coherence is proven for specific classes of nilmanifolds.

Extension of previous results from tori to nilmanifolds.

Provides new insights into the structure of partially hyperbolic systems on nilmanifolds.

Abstract

The purpose of this article is to obtain dynamically coherence of partially hyperbolic diffeomorphisms in certain classes of Anosov diffeomorphisms on nilmanifolds, extending a result due to T. Fisher, R. Potrie and M. Sambarino [FPS] on the torus.