On dynamical coherence of partially hyperbolic flows

TL;DR

This paper introduces the concept of dynamical coherence for partially hyperbolic flows on compact manifolds and proves it under specific foliation conditions, advancing understanding of flow structures.

Contribution

It defines dynamical coherence for flows and establishes conditions for its existence based on foliation properties, a novel extension from discrete to continuous-time systems.

Findings

Dynamical coherence can be achieved under certain foliation conditions.

Existence of a compact foliation with trivial holonomy ensures coherence.

The work extends discrete hyperbolic theory to flows.

Abstract

In this paper, we introduce the notion of dynamical coherence for a partially hyperbolic flow $(\varphi^t)$ on a smooth compact manifold $M$, and prove it under the assumption that there exists a compact foliation with trivial holonomy which integrates the subcenter distribution.