Dynamical coherence in isotopy classes of fibered lifted partially hyperbolic diffeomorphisms

TL;DR

This paper introduces fibered lifted partially hyperbolic diffeomorphisms and proves their dynamic coherence and stability properties within isotopy classes, advancing understanding of their structural behavior.

Contribution

It establishes the dynamic coherence and leaf conjugacy stability for isotopic classes of fibered lifted partially hyperbolic diffeomorphisms, a novel class in the field.

Findings

Any isotopic partially hyperbolic diffeomorphism to a fibered lifted one is dynamically coherent.

Connected components of fibered lifted partially hyperbolic diffeomorphisms have leaf conjugate structures.

The results provide global stability insights for these dynamical systems.

Abstract

We introduce the notion of \textit{fibered lifted partially hyperbolic diffeomorphisms} and we prove that any partially hyperbolic diifeomorphism isotopic to a fibered lifted one where the isotopy take place inside partially hyperbolic systems is \textit{dynamically coherent.} Moreover we prove some global stability result: every two partially hyperbolic diffeomorphisms in the same connected component of a fibered lifted partially hyperbolic diffeomorphisms, are leaf conjugate.