On partially hyperbolic diffeomorphisms in dimension three via a notion of autonomous dynamics

TL;DR

This paper introduces a new concept of autonomous dynamics to study the rigidity of partially hyperbolic diffeomorphisms on three-dimensional manifolds, providing insights into their structural stability under certain smoothness conditions.

Contribution

It proposes a novel notion of autonomous systems and applies it to establish rigidity results for partially hyperbolic diffeomorphisms in three dimensions.

Findings

Rigidity results for partially hyperbolic diffeomorphisms

Introduction of autonomous dynamics concept

Application to three-manifolds with smooth framing

Abstract

We introduce a notion of autonomous dynamical systems and apply it to prove rigidity of partially hyperbolic diffeomorphisms on closed compact three-manifolds under some smoothness hypothesis of their associated framing.