Symmetric designs on Lie algebras and interactions of hamiltonian systems.

TL;DR

This paper explores how symmetric designs on Lie algebras can be used to model non-Hamiltonian interactions in dynamical systems, revealing potential for describing complex periodic and chaotic behaviors.

Contribution

It introduces a novel approach using symmetric designs on Lie algebras to analyze non-Hamiltonian systems, extending beyond Jordan algebras.

Findings

Symmetric designs on Lie algebras can model almost periodic and chaotic systems.

Systems with additional identities exhibit simpler behavior.

Algebraic structures beyond Lie algebras are useful for dynamical system analysis.

Abstract

Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie algebras beyond Jordan ones may be useful for a description of almost periodic, asymptotically periodic, almost asymptotically periodic, and, possibly, more chaotic systems. However, the behaviour of systems related to symmetric designs with additional identities is simpler than for general ones from different points of view. These facts confirm a general thesis that various algebraic structures beyond Lie algebras may be regarded as certain characteristics for a wide class of dynamical systems.