Partially Dominated Splittings

TL;DR

This paper introduces the concept of partially dominated splittings as a weaker form of domination for flows and establishes an equivalence with dominated splittings of the linear Poincare flow on nonsingular compact invariant sets.

Contribution

It defines partially dominated splittings and proves their equivalence to dominated splittings of the linear Poincare flow, extending the understanding of flow dynamics.

Findings

Partially dominated splittings exist over nonsingular compact invariant sets.

Equivalence established between partially dominated splittings and dominated splittings of the linear Poincare flow.

Provides a new framework for analyzing flow stability and structure.

Abstract

We propose a weak form of domination, called partially dominated splitting and the main result is that there is a partially dominated splitting over a nonsingular compact invariant set for a flow if, and only if, the associated linear Poincare flow has a dominated splitting