Equivariant symplectic difference schemes and generating functions

DOI10.1016/0167-2789(91)90154-2zbMath0735.58018OpenAlexW2045070019MaRDI QIDQ1176810

Zhong Ge

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0167-2789(91)90154-2

zbMATH Keywords

Hamiltonian systemfirst integralsymplectic difference scheme

Mathematics Subject Classification ID

Hamilton's equations (70H05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (15)

Hamiltonian truncation of the shallow water equation ⋮ Poisson Integrators Based on Splitting Method for Poisson Systems ⋮ Some aspects of Hamiltonian systems and symplectic algorithms ⋮ Momentum conserving symplectic integrators ⋮ Equivariant constrained symplectic integration ⋮ A note for Lie-Poisson Hamilton-Jacobi equation and Lie-Poisson integrator ⋮ The limits of Hamiltonian structures in three-dimensional elasticity, shells, and rods ⋮ On the geometry of the Hamilton-Jacobi equation and generating functions ⋮ Hamilton-Jacobi theory, symmetries and coisotropic reduction ⋮ Accurate and efficient simulation of rigid-body rotations. ⋮ Poisson integrators ⋮ Symplectic methods for the nonlinear Schrödinger equation ⋮ Generating functions for dynamical systems with symmetries, integrals, and differential invariants ⋮ Partitioned averaged vector field methods ⋮ On the invariance of generating functions for symplectic transformations

Cites Work

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• Hamiltonian differencing of fluid dynamics
• Coisotropic calculus and Poisson groupoids
• The moment map and collective motion
• Integrators for Lie-Poisson dynamical systems
• Reduction of symplectic manifolds with symmetry
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Symplectic integration of Hamiltonian systems
• Symplectic groupoids and Poisson manifolds

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