EFFICIENT INTEGRATION OF THE VARIATIONAL EQUATIONS OF MULTIDIMENSIONAL HAMILTONIAN SYSTEMS: APPLICATION TO THE FERMI–PASTA–ULAM LATTICE

DOI10.1142/S0218127412502161zbMath1258.65104arXiv1104.3127OpenAlexW3101703694MaRDI QIDQ4907084

Siegfried Eggl, Enrico Gerlach, Charalampos Skokos

Publication date: 1 March 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.3127

zbMATH Keywords

numerical integrationHamiltonian systemsvariational equationsGALI methodtangent map method

Mathematics Subject Classification ID

Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (7)

Frequency Map Analysis of Spatiotemporal Chaos in the Nonlinear Disordered Klein–Gordon Lattice ⋮ Identifying localized and spreading chaos in nonlinear disordered lattices by the generalized alignment index (GALI) method ⋮ Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using \(q\)-statistics ⋮ Splitting schemes and energy preservation for separable Hamiltonian systems ⋮ On the Behavior of the Generalized Alignment Index (GALI) Method for Regular Motion in Multidimensional Hamiltonian Systems ⋮ Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions ⋮ Complex statistics and diffusion in nonlinear disordered particle chains

Cites Work

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• Application of the GALI method to localization dynamics in nonlinear systems
• Performance of the Taylor series method for ODEs/DAEs
• Solving Ordinary Differential Equations I
• Integration of the elliptic restricted three-body problem with Lie series
• General theory of fractal path integrals with applications to many-body theories and statistical physics
• Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits
• Scaling with System Size of the Lyapunov Exponents for the Hamiltonian Mean Field Model
• PROBING THE LOCAL DYNAMICS OF PERIODIC ORBITS BY THE GENERALIZED ALIGNMENT INDEX (GALI) METHOD
• High-order symplectic integrators for perturbed Hamiltonian systems

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