On the fixed points set of differential systems reversibilities

TL;DR

This paper extends previous results on mirror symmetries of planar systems to measure-preserving non-linear reversibilities in higher-dimensional systems, removing the need for analyticity and nondegeneracy assumptions.

Contribution

It generalizes the understanding of reversibility fixed points from planar to n-dimensional systems without requiring analyticity or nondegeneracy.

Findings

Extended fixed point results to higher dimensions

Removed analyticity and nondegeneracy constraints

Applicable to measure-preserving non-linear systems

Abstract

We extend a result proved in \cite{Col} for mirror symmetries of planar systems to measure-preserving non-linear reversibilities of $n$-dimensional systems, dropping the analyticity and nondegeneracy conditions.