A functional analysis approach to Arnold diffusion
From MaRDI portal
Publication:697656
DOI10.1016/S0294-1449(01)00084-1zbMath1087.37048OpenAlexW2046384034MaRDI QIDQ697656
Massimiliano Berti, Philippe Bolle
Publication date: 17 September 2002
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_2002__19_4_395_0
variational methodsnonlinear functional analysisArnold diffusionheteroclinic orbitssplitting of separatricesshadowing theorem
Related Items
Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion, Existence of homoclinic solutions to periodic orbits in a center manifold, Topological shadowing methods in arnold diffusion: weak torsion and multiple time scales, Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems, Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem, 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, Drift in phase space: A new variational mechanism with optimal diffusion time, An example of Arnold diffusion for near-integrable Hamiltonians, A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold, Homoclinic solutions to invariant tori in a center manifold, Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems, Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders, Arnold diffusion in a neighborhood of strong resonances, Arnol′d Diffusion in a Pendulum Lattice, Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows., Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation, A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results, 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, An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum, Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems
Cites Work
- Arnold diffusion: a variational construction
- An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
- On the distribution of free path lengths for the periodic Lorentz gas
- Separatrix splitting for systems with three time scales
- A proof of the exponentially small transversality of the separatrices for the standard map
- Arnold's diffusion in isochronous systems
- A \(\lambda\)-lemma for partially hyperbolic tori and the obstruction property
- Exponentially small splitting of separatrices under fast quasiperiodic forcing
- Homoclinics: Poincaré-Melnikov type results via a variational approach
- Homoclinics and chaotic behaviour for perturbed second order systems
- Fast Arnold diffusion in systems with three time scales
- Multidimensional symplectic separatrix maps
- Separatrix splitting for a high-frequency perturbation of the pendulum.
- Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
- Periodic orbits and Arnold diffusion
- On the double pendulum: An example of double resonant situations
- Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems
- On homoclinic splitting problems
- MEL'NIKOV'S APPROXIMATION DOMINANCE: SOME EXAMPLES
- On the splitting of invariant manifolds in multidimensional near-integrable Hamiltonian systems
- A proof of existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems
- An approach to arnold's diffusion through the calculus of variations
- Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scale systems
- Upper bounds on Arnold diffusion time via Mather theory
- Infinite number of homoclinic orbits to hyperbolic invariant tori of Hamiltonian systems
- On a homoclinic splitting problem
- Melnikov method and exponentially small splitting of separatrices
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
