From Hamiltonian perturbation theory to symplectic integrators and back

DOI10.1016/S0168-9274(98)00074-9zbMath1028.37035MaRDI QIDQ1294537

Giancarlo Benettin, Francesco Fassoò

Publication date: 9 December 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical experimentsHamiltonian perturbation theorysymplectic integratorsnearly integrable Hamiltonian systemsmolecular collision problems

Mathematics Subject Classification ID

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (5)

A numerical study of the topology of normally hyperbolic invariant manifolds supporting Arnold diffusion in quasi-integrable systems ⋮ On an asymptotic method for computing the modified energy for symplectic methods ⋮ On the numerical integration of FPU-like systems ⋮ A symplectic, symmetric algorithm for spatial evolution of particles in a time-dependent field ⋮ Local and global diffusion along resonant lines in discrete quasi-integrable dynamical systems

Cites Work

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• The separation of motions in systems with rapidly rotating phase
• Canonical Runge-Kutta methods
• On the conservation of adiabatic invariants for a system of coupled rotators
• The life-span of backward error analysis for numerical integrators
• On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
• On the Landau-Teller approximation for energy exchanges with fast degrees of freedom
• A rigorous implementation of the Jeans - Landau - Teller approximation for adiabatic invariants

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