Bi-Hamiltonian Structures of Chaotic Dynamical Systems in 3D

TL;DR

This paper investigates the Poisson structures of several 3D chaotic dynamical systems, revealing that they all possess bi-Hamiltonian structures contingent on parameter values, which enhances understanding of their geometric properties.

Contribution

It demonstrates that key chaotic systems in three dimensions admit bi-Hamiltonian structures, a novel insight into their geometric and algebraic properties.

Findings

All studied systems have bi-Hamiltonian structures.

Bi-Hamiltonian structures depend on system parameters.

Provides a geometric perspective on chaotic dynamics.

Abstract

We study Poisson structures of dynamical systems with three degrees of freedom which are known for their chaotic properties, namely L\"u, modified L\"u, Chen, $T$ and Qi systems. We show that all these flows admit bi-Hamiltonian structures depending on the values of their parameters.