Arnold diffusion in Hamiltonian systems on infinite lattices (Q6587582)

scientific article; zbMATH DE number 7896923

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English	Arnold diffusion in Hamiltonian systems on infinite lattices	scientific article; zbMATH DE number 7896923

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scholarly article

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title

Arnold diffusion in Hamiltonian systems on infinite lattices (English)

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Communications on Pure and Applied Mathematics

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publication date

14 August 2024

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zbMATH Keywords

system of infinitely many penduli

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Arnold diffusion mechanism

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invariant manifold theory

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hyperbolic tori

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Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems

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On metastability in FPU

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Invariant Objects on Lattice Systems with Decaying Interactions

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The dynamics of pseudographs in convex Hamiltonian systems

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Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders

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Drift in phase space: A new variational mechanism with optimal diffusion time

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A functional analysis approach to Arnold diffusion

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Fast Arnold diffusion in systems with three time scales

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An approach to arnold's diffusion through the calculus of variations

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Localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction

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Q2737644

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Stable manifolds and the Perron–Irwin method

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The Lipschitzian core of some invariant manifold theorems

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Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems

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Existence of diffusion orbits in a priori unstable Hamiltonian systems

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Second order Hamiltonian equations on \(\mathbb{T}^ \infty\) and almost- periodic solutions

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Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation

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A \(\lambda\)-lemma for partially hyperbolic tori and the obstruction property

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Asymptotic Localization of Energy in Nondisordered Oscillator Chains

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A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model

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Geometric properties of the scattering map of a normally hyperbolic invariant manifold

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Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion

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Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method

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Dynamical systems on lattices with decaying interaction. I: A functional analysis framework

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Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds

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Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices

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Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma

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Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit

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Localization in disordered, nonlinear dynamical systems

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Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction

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Arnold diffusion in a priori chaotic symplectic maps

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A KAM theorem for Hamiltonian networks with long ranged couplings

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Localization in one-dimensional quasi-periodic nonlinear systems

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A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results

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Diffusing orbits along chains of cylinders

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Chaotic-like transfers of energy in Hamiltonian PDEs

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Growth of Sobolev norms for the analytic NLS on \(\mathbb{T}^2\)

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Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation

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Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation

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Long-time instability and unbounded Sobolev orbits for some periodic nonlinear Schrödinger equations

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MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS

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Growth of Sobolev norms for the quintic NLS on \(\mathbb T^2\)

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Results on normal forms for FPU chains

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Resonant normal form for even periodic FPU chains

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Stable manifolds for hyperbolic sets

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On energy transferring in a periodic pendulum lattice with analytic weak couplings

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Smooth dependence of thermodynamic limits of SRB-measures

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An example of Arnold diffusion for near-integrable Hamiltonians

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Geometry of Arnold Diffusion

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Arnol′d Diffusion in a Pendulum Lattice

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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom

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Q4320141

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The analytic invariants of an area-preserving mapping near a hyperbolic fixed point

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Q3952851

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An inclination lemma for normally hyperbolic manifolds with an application to diffusion

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Evolution of slow variables in<b><i>a priori</i></b>unstable Hamiltonian systems

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Arnold diffusion far from strong resonances in multidimensional a priori unstable Hamiltonian systems

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Bounds on the trajectories of a system of weakly coupled rotators

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On the elimination of non-resonance harmonics

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On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range

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Construction of quasi-periodic breathers via KAM technique

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Identifiers

Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6587582