Reversible-equivariant systems and matricial equations

TL;DR

This paper classifies finite group representations related to reversible-equivariant vector fields in four dimensions, using algebraic solutions of matrix equations and group theory tools to derive simplified normal forms.

Contribution

It introduces a novel classification of finite group representations for reversible-equivariant systems in , employing algebraic matrix equations and group theory methods.

Findings

Classified representations of finite groups of order less than 9

Derived simplified Belitskii normal forms for each class

Identified involutions relevant to reversible-equivariant vector fields

Abstract

This paper uses tools in group theory and symbolic computing to give a classification of the representations of finite groups with order lower than 9 that can be derived from the study of local reversible-equivariant vector fields in $\rn{4}$. The results are obtained by solving algebraically matricial equations. In particular, we exhibit the involutions used in a local study of reversible-equivariant vector fields. Based on such approach we present, for each element in this class, a simplified Belitiskii normal form.