Belitskii's canonical forms of linear dynamical systems

TL;DR

This paper determines all indecomposable canonical forms of linear systems up to dimension 4 using Belitskii's algorithm, providing an effective method to compute the dimensions of equivalence classes of such systems.

Contribution

It offers a complete classification of low-dimensional linear systems' canonical forms and introduces a practical approach to calculate their equivalence class dimensions.

Findings

All indecomposable canonical forms for systems of dimension ≤ 4 are identified.

A method to compute dimensions of equivalence classes using Belitskii's canonical forms is proposed.

The classification aids in understanding the structure of linear dynamical systems.

Abstract

In the note, all indecomposable canonical forms of linear systems with dimension less than or equal to $4$ are determined based on Belitskii's algorithm. As an application, an effective way to calculate dimensions of equivalence classes of linear systems is given by using Belitskii's canonical forms.