On the global behavior of linear flows

TL;DR

This paper investigates the conditions under which subbundles in the Selgrade decomposition of linear flows on vector bundles form chain transitive subsets on the associated Poincaré sphere bundle, enhancing understanding of their global behavior.

Contribution

It provides new criteria linking the Selgrade decomposition to chain transitivity on Poincaré sphere bundles for linear flows.

Findings

Identifies conditions for chain transitivity in subbundles

Connects Selgrade decomposition with global flow behavior

Offers insights into the structure of linear flows on vector bundles

Abstract

For linear flows on vector bundles, it is analyzed when subbundles in the Selgrade decomposition yield chain transitive subsets for the induced flow on the associated Poincar\'e sphere bundle.