A class of Lorenz-type systems, their factorizations and extensions

TL;DR

This paper introduces a new representation of the Lorenz system using topological covering-coloring, leading to factorized and extended Lorenz-type systems with arbitrary symmetries, offering a more fundamental perspective.

Contribution

It presents a novel topological approach to factorize and extend Lorenz systems, generalizing to systems with arbitrary symmetries.

Findings

Factorization of Lorenz system via topological coloring

Introduction of Z_n extensions for Lorenz-type systems

Generalization to systems with arbitrary symmetries

Abstract

It is well known that the Lorenz system has $Z_2$-symmetry. Using introducted in math.DS/0105147 topological covering-coloring a new representation for the Lorenz system is obtained. Deleting coloring leads to the factorized Lorenz system that is in a sense more fundamental than the original one. Finally, $Z_n$ extensions define a class of Lorenz-type systems. The approach admits a natural generalization for regular and chaotic systems with arbitrary symmetries.