Topological Conjugacy of Non-hyperbolic Linear Flows

TL;DR

This paper provides an elementary, self-contained proof for classifying linear flows on ^n up to topological conjugacy, simplifying previous complex proofs by Kuiper and Ladis using basic linear algebra and topology.

Contribution

It offers a new, accessible proof for the topological conjugacy classification of linear flows, building on Kuiper's ideas with simplified techniques.

Findings

Complete classification of linear flows on ^n up to topological conjugacy

Elementary proof using linear algebra and basic topology

Simplifies previous complex proofs by Kuiper and Ladis

Abstract

The topological equivalence classification for linear flows on $\mathbb{R}^n$ had been completely solved by Kuiper and independently Ladis in 1973. However, Ladis' proof was published in a Russian journal which isn't easily available, Kuiper's proof is more topological and a little bit subtle. Aiming at topological conjugacy classification, mainly based on the ideas of Kuiper, we introduce other techniques and try to present an elementary and self-contained proof just using linear algebra and elementary topology.