On a Lie algebraic structure associated with a non-linear dynamical system

TL;DR

This paper explores a specific Lie algebraic structure linked to non-linear dynamical systems, including the Heisenberg algebra, and introduces an evapotranspiration function to distinguish these systems, with homological analysis providing topological insights.

Contribution

It calculates a family of minimal dimension Lie algebras associated with non-linear dynamical systems, incorporating the evapotranspiration function and homological properties.

Findings

Lie algebras contain the Heisenberg algebra

Evapotranspiration function distinguishes vector fields

Euler characteristic computed via Koszul homology

Abstract

A family of Lie algebras of minimal dimension associated with vector fields that define a non-linear dynamical system is calculated. These Lie algebras contain the Heinsenberg algebra. An element that distinguishes these vector fields is called evapotranspiration function. This function can be calculated solving equations in partial derivatives that arise in determining the Heinsenberg algebra. Using Kozsul homology for this Lie algebras, Euler characteristic is calculated.