Arnol′d Diffusion in a Pendulum Lattice
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Publication:5413646
DOI10.1002/cpa.21509zbMath1382.37062arXiv1104.0580OpenAlexW2119007659MaRDI QIDQ5413646
Maria Saprykina, Mark Levi, Vadim Yu. Kaloshin
Publication date: 30 April 2014
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1104.0580
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Ordinary lattice differential equations (34A33)
Related Items (8)
On energy transferring in a periodic pendulum lattice with analytic weak couplings ⋮ Existence of diffusion orbits in a lattice system ⋮ Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems ⋮ A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems ⋮ Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders ⋮ An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension ⋮ Bouncing in gravitational field ⋮ Instabilities of invariant quasi-periodic tori
Cites Work
- Weak chaos in the disordered nonlinear Schrödinger chain: destruction of Anderson localization by Arnold diffusion
- Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians
- A functional analysis approach to Arnold diffusion
- Results on normal forms for FPU chains
- Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
- Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation
- Localization in disordered, nonlinear dynamical systems
- Arnold's diffusion with two resonances
- A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2\)
- Shadowing property of geodesics in Hedlund's metric
- An example of Arnold diffusion for near-integrable Hamiltonians
- Geometry of Arnold Diffusion
- Unbounded growth of energy in nonautonomous Hamiltonian systems
- An approach to arnold's diffusion through the calculus of variations
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