Results on normal forms for FPU chains

DOI10.1007/s00220-007-0387-zzbMath1168.70005OpenAlexW1992146588MaRDI QIDQ934597

Andreas Henrici, Thomas Kappeler

Publication date: 30 July 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://www.zora.uzh.ch/id/eprint/7209/10/ZORA_NL_7209.pdf

zbMATH Keywords

Birkhoff normal formcomplete integrabilityresonant normal form

Mathematics Subject Classification ID

Dynamics of a system of particles, including celestial mechanics (70F99) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Normal forms for nonlinear problems in mechanics (70K45)

Related Items (14)

On energy transferring in a periodic pendulum lattice with analytic weak couplings ⋮ Periodic Klein-Gordon chains with three particles in 1:2:2 resonance ⋮ Resonant normal form for even periodic FPU chains ⋮ Wave turbulence and thermalization in one-dimensional chains ⋮ Energy exchange and transition to localization in the asymmetric Fermi-pasta-Ulam oscillatory chain ⋮ Exact discrete resonances in the Fermi-Pasta-Ulam-Tsingou system ⋮ Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit ⋮ On intense energy exchange and localization in periodic FPU dimer chains ⋮ Arnol′d Diffusion in a Pendulum Lattice ⋮ Global dynamical properties of the Fermi-Pasta-Ulam system ⋮ Universal route to thermalization in weakly-nonlinear one-dimensional chains ⋮ Near-integrability of periodic Klein-Gordon lattices ⋮ Korteweg–de Vries and Fermi–Pasta–Ulam–Tsingou: asymptotic integrability of quasi unidirectional waves ⋮ Symmetries of the periodic Toda lattice, with an application to normal forms and perturbations of the lattice with Dirichlet boundary conditions

Cites Work

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• Resonant normal form for even periodic FPU chains
• Proof of Nishida's conjecture on anharmonic lattices
• On metastability in FPU
• Theory of nonlinear lattices.
• Direction-reversing traveling waves in the even Fermi-Pasta-Ulam lattice
• Integrability of hamiltonian systems on cantor sets
• Global Birkhoff coordinates for the periodic Toda lattice
• KAM theory: The legacy of Kolmogorov's 1954 paper
• The Fermi–Pasta–Ulam problem: Fifty years of progress
• Korteweg–de Vries equation and energy sharing in Fermi–Pasta–Ulam
• Symmetry and resonance in periodic FPU chains

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