Lie-Poisson description of Hamiltonian ray optics

DOI10.1016/0167-2789(91)90231-WzbMath0756.58028OpenAlexW2050786655MaRDI QIDQ1181167

Darryl D. Holm, Kurt Bernardo Wolf

Publication date: 27 June 1992

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(91)90231-w

zbMATH Keywords

Hamiltonian systemgeometrical opticsaxi-symmetric mediumLie-Poisson dynamical system

Mathematics Subject Classification ID

Lasers, masers, optical bistability, nonlinear optics (78A60) Stability theory for smooth dynamical systems (37C75)

Related Items

Nekhoroshev and KAM stabilities in generalized Hamiltonian systems ⋮ New global solutions of the Jacobi partial differential equations ⋮ On the generalized Hamiltonian structure of 3D dynamical systems ⋮ A constant of motion in 3D implies a local generalized Hamiltonian structure. ⋮ Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems ⋮ New solutions of the Jacobi equations for three-dimensional Poisson structures ⋮ Characterization and global analysis of a family of Poisson structures ⋮ One solution of the 3D Jacobi identities allows determining an infinity of them ⋮ Simple evaluation of Casimir invariants in finite-dimensional Poisson systems

Cites Work

• Unnamed Item
• The local structure of Poisson manifolds
• Homoclinic chaos for ray optics in a fiber
• Differential forms. With applications to the physical sciences
• Nonlinear stability of fluid and plasma equilibria
• Reduction, symmetry, and phases in mechanics
• Symplectic connections and the linearisation of Hamiltonian systems