Poisson geometry of the Maxwell-Bloch top system and stability problem

2014/01/03 by Mihai Ivan, Ivan, Mihai
Computer Science · Mathematics · Physics and Astronomy · #34H05 #37C20 #37C75 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.DS #msc:34H05 #msc:37C20 #msc:37C75

paper · pdf · doi:10.48550/arxiv.1401.0641

12 pages, no figure

arxiv created 2014/01/03 · openalex publication_date 2014/01/03 · arxiv updated 2014/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dynamics of Maxwell-Bloch top system, that includes Maxwell-Bloch and Lorenz-Hamilton equations as particular cases, is studied in the framework Poisson geometry. Constants of motion as well as the relation of solution to that of pendulum are presented. Equilibrium states are determined and their complete stability analysis are performed. Results are applied to an optimal control problem on the Lie group G4.

Related

• On some dynamical and geometrical properties of the Maxwell-Bloch equations with a quadratic control
• Bloch Motions and Spinning Tops
• Rank change in Poisson dynamical systems
• On the dynamics of a Hamilton-Poisson system
• The Rigid Body Dynamics in an ideal fluid: Clebsch Top and Kummer surfaces