A minimal-variable symplectic method for isospectral flows

DOI10.1007/s10543-019-00792-1zbMath1448.37107arXiv1904.07117OpenAlexW3098935949WikidataQ126561168 ScholiaQ126561168MaRDI QIDQ2192599

Milo Viviani

Publication date: 17 August 2020

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.07117

zbMATH Keywords

isospectral flowHeisenberg spin chainsymplectic Runge-Kutta methodsgeneralized rigid bodyLie-Poisson integratorBrockett flowpoint-vortex on the hyperbolic plane

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Momentum maps; symplectic reduction (53D20) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Completely integrable discrete dynamical systems (37J70)

Related Items (5)

Integrability of point-vortex dynamics via symplectic reduction: a survey ⋮ An algebraic approach to the spontaneous formation of spherical jets ⋮ Solving cubic matrix equations arising in conservative dynamics ⋮ A Casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics ⋮ An efficient geometric method for incompressible hydrodynamics on the sphere

Cites Work

• Unnamed Item
• Unnamed Item
• Point vortices on the sphere: stability of symmetric relative equilibria
• Note on the integration of Euler's equations of the dynamics of an \(n\)-dimensional rigid body
• Topological methods in hydrodynamics
• Lie-Butcher theory for Runge-Kutta methods
• Lie-Poisson methods for isospectral flows
• Point vortices on hyperbolic sphere
• Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• Point vortices on the hyperbolic plane
• A minimal-variable symplectic integrator on spheres
• Vortex Methods. II: Higher Order Accuracy in Two and Three Dimensions
• Numerical solution of isospectral flows
• Relative equilibria of point vortices on the hyperbolic sphere
• Geometric Numerical Integration
• Lie groups beyond an introduction

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