On the classification of finite-dimensional linear flows

TL;DR

This paper provides new elementary proofs for classifying finite-dimensional linear flows, emphasizing the roles of linearity and smoothness, and clarifies their importance compared to previous literature.

Contribution

It introduces self-contained, elementary proofs for topological and smooth classification theorems of linear flows, highlighting the fundamental roles of linearity and smoothness.

Findings

Simplified proofs for classification theorems

Clearer illustration of linearity and smoothness roles

Enhanced understanding of linear flow structures

Abstract

New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the fundamental roles of linearity and smoothness more clearly than does the existing literature.