Arnold diffusion in Hamiltonian systems on infinite lattices

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Cites Work

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Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion
Growth of Sobolev norms for the analytic NLS on \(\mathbb{T}^2\)
Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
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Dynamical systems on lattices with decaying interaction. I: A functional analysis framework
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A functional analysis approach to Arnold diffusion
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Localization in disordered, nonlinear dynamical systems
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Smooth dependence of thermodynamic limits of SRB-measures
Fast Arnold diffusion in systems with three time scales
Bounds on the trajectories of a system of weakly coupled rotators
Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
Chaotic-like transfers of energy in Hamiltonian PDEs
Diffusing orbits along chains of cylinders
On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range
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Arnold diffusion in a priori chaotic symplectic maps
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Long-time instability and unbounded Sobolev orbits for some periodic nonlinear Schrödinger equations
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Arnold diffusion far from strong resonances in multidimensionala prioriunstable Hamiltonian systems
MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
An inclination lemma for normally hyperbolic manifolds with an application to diffusion
Asymptotic Localization of Energy in Nondisordered Oscillator Chains
The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
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An example of Arnold diffusion for near-integrable Hamiltonians
Geometry of Arnold Diffusion
The dynamics of pseudographs in convex Hamiltonian systems
The Lipschitzian core of some invariant manifold theorems
Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma
Evolution of slow variables ina prioriunstable Hamiltonian systems
Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit
An approach to arnold's diffusion through the calculus of variations
Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction
Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
Invariant Objects on Lattice Systems with Decaying Interactions
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Stable manifolds and the Perron–Irwin method
A KAM theorem for Hamiltonian networks with long ranged couplings
Arnol′d Diffusion in a Pendulum Lattice
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