Linearization of Cohomology-free Vector Fields

TL;DR

This paper investigates cohomology-free vector fields on compact manifolds and demonstrates that such fields can be embedded into linear flows on Abelian groups, revealing a structural property of these dynamical systems.

Contribution

It establishes a new connection between cohomology-free vector fields and linear flows on Abelian groups, providing a novel structural insight.

Findings

Cohomology-free vector fields can be embedded into linear flows on Abelian groups.

The study offers a characterization of cohomology-free vector fields.

Provides a framework for understanding the structure of certain dynamical systems.

Abstract

We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group.