Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems

DOI10.1007/s11425-018-9311-7zbMath1400.37068arXiv1805.03425OpenAlexW2802680271MaRDI QIDQ1989888

Zhaodong Ding, Zaijiu Shang

Publication date: 29 October 2018

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.03425

zbMATH Keywords

KAM theoryHamiltonian systeminvariant torisymplectic integratorRüssmann's non-degeneracytwist symplectic mapping

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Stability and convergence of numerical methods for ordinary differential equations (65L20) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Numerical nonlinear stabilities in dynamical systems (65P40)

Cites Work

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• Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems
• A KAM theorem for a class of nearly integrable symplectic mappings
• On elliptic lower dimensional tori in Hamiltonian systems
• Some aspects of Hamiltonian systems and symplectic algorithms
• The life-span of backward error analysis for numerical integrators
• On the qualitative behaviour of symplectic integrators. II: Integrable systems
• Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• A note on the KAM theorem for symplectic mappings
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• KAM theorem of symplectic algorithms for Hamiltonian systems
• On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
• KAM-stable Hamiltonians
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• The hyperbolic invariant tori of symplectic mappings
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Integrability of hamiltonian systems on cantor sets
• On the KAM and Nekhoroshev theorems for symplectic integrators and implications for error growth
• Nonlinear Stability Analysis of Area-Preserving Integrators
• Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems
• Geometric Numerical Integration

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