KAM TORI AND ABSENCE OF DIFFUSION OF A WAVE-PACKET IN THE 1D RANDOM DNLS MODEL

DOI10.1142/S0218127411029677zbMath1248.37053OpenAlexW2115411720MaRDI QIDQ3165825

Serge Aubry

Publication date: 19 October 2012

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

Full work available at URL: https://doi.org/10.1142/s0218127411029677

zbMATH Keywords

KAM toriDNLS modelsinfinite disordered systems

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Random dynamical systems (37H99) Lattice dynamics; integrable lattice equations (37K60)

Related Items (7)

Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices ⋮ 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 ⋮ Scaling of energy spreading in a disordered Ding-Dong lattice ⋮ High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation ⋮ Complex statistics and diffusion in nonlinear disordered particle chains

Cites Work

• Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems
• Small divisors with spatial structure in infinite dimensional Hamiltonian systems
• Breathers in nonlinear lattices: existence, linear stability and quantization
• Long time Anderson localization for the nonlinear random Schrödinger equation
• Anomalous thermostat and intraband discrete breathers
• Strange attractors that are not chaotic
• Localization in disordered, nonlinear dynamical systems
• Transition spectra of dynamical systems
• Discrete breathers: localization and transfer of energy in discrete Hamiltonian nonlinear systems
• Solved Problems in Lagrangian and Hamiltonian Mechanics
• Perturbation theory for the nonlinear Schrödinger equation with a random potential
• Existence and stability of quasiperiodic breathers in the discrete nonlinear Schrödinger equation
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• STICKINESS EFFECTS IN CONSERVATIVE SYSTEMS

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