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

DOI10.1016/S0021-7824(03)00032-1zbMath1025.37037arXivmath/0205307OpenAlexW2169122492MaRDI QIDQ1408897

Luca Biasco, Philippe Bolle, Massimiliano Berti

Publication date: 25 September 2003

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0205307

zbMATH Keywords

perturbation theory variational methods nonlinear functional analysis Arnold diffusion shadowing theorem

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items

Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion, Arnold diffusion in a priori chaotic symplectic maps, Existence of homoclinic solutions to periodic orbits in a center manifold, Topological shadowing methods in arnold diffusion: weak torsion and multiple time scales, Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings, Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem, Filling times for linear flow on the torus with truncated Diophantine conditions: a brief review and new proof, Fast drift and diffusion in a class of isochronous systems with the windows method, Semi-analytic computations of the speed of Arnold diffusion along single resonances in a priori stable Hamiltonian systems, Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the <scp>Three‐Body</scp> Problem, Arnold Diffusion in a Model of Dissipative System, A geometric mechanism of diffusion: rigorous verification in a priori unstable Hamiltonian systems, On the topology of nearly-integrable Hamiltonians at simple resonances, Global diffusion on a tight three-sphere, Arnold diffusion for a complete family of perturbations, A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold, Effective stability for Gevrey and finitely differentiable prevalent Hamiltonians, Speed of Arnold diffusion for analytic Hamiltonian systems, The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks, Homoclinic solutions to invariant tori in a center manifold, Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems, Geometric properties of the scattering map of a normally hyperbolic invariant manifold, Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders, Perturbations of geodesic flows by recurrent dynamics, Arnold diffusion in a neighborhood of strong resonances, The dynamics of pseudographs in convex Hamiltonian systems, Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows., A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results, The numerical detection of the Arnold web and its use for long-term diffusion studies in conservative and weakly dissipative systems, A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems, Ergodization time for linear flows on tori via geometry of numbers, Periodic orbits accumulating onto elliptic tori for the \((N + 1)\)-body problem, Variational construction of positive entropy invariant measures of Lagrangian systems and Arnold diffusion, Unnamed Item, A numerical study of Arnold diffusion in a priori unstable systems, Diffusing orbits along chains of cylinders, Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems

Cites Work