Complete transversals of reversible equivariant singularities of vector fields

TL;DR

This paper develops algebraic formulas using group representation theory to compute complete transversals and normal forms of singularities in vector fields, aiding local analysis of symmetric dynamics.

Contribution

It introduces a systematic algebraic method for computing complete transversals and normal forms in reversible equivariant singularities using group representation theory.

Findings

Provides explicit algebraic formulas for transversals

Enables direct computation of normal forms

Facilitates analysis of symmetric dynamical systems

Abstract

We use group representation theory to give algebraic formulae to compute complete transversals of singularities of vector fields, either in the nonsymmetric or in the reversible equivariant contexts. This computation produces normal forms directly, which are used sistematically in the local analysis of symmetric dynamics.