Symmetry of Quadratic Homogeneous Differential Systems

TL;DR

This paper investigates the symmetry groups of quadratic homogeneous first-order differential systems, analyzing their Lie algebras and differential invariants to deepen understanding of their structural properties.

Contribution

It characterizes the symmetry groups and invariants of quadratic homogeneous differential systems using point and contact transformations.

Findings

Identified the Lie algebras associated with these systems

Derived the independent differential invariants

Provided a framework for symmetry analysis of quadratic systems

Abstract

In this paper, the symmetry group of a differential system of n quadratic homogeneous first order ODEs of n variables is studied. For this purpose, we consider the action of both point and contact transformations to signify the corresponding Lie algebras. We also find the independent differential invariants of these actions.