Fast Arnold Diiusion in Systems with Three Time Scales
نویسنده
چکیده
We consider the problem of Arnold Diiusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diiusion takes place with fast (polynomial) speed, even though the \splitting determinant" is exponentially small.
منابع مشابه
Upper Bounds on Arnold Diiusion Time via Mather Theory
We consider several Hamiltonian systems for which the existence of Arnold's mechanism for diiusion (whiskered tori, transition ladder, etc.) has been proven. By means of Mather theory we show that the diiusion time may be bounded by a power of the homoclinic splitting.
متن کاملThree-dimensional Cellular Automata for Reaction-Diffusion Systems
Cellular automata for reaction-diiusion systems are eecient enough to make the simulation of large three-dimensional systems feasible. The principal construction mechanisms used here are not much diierent from those for two-dimensional cellular automata. Diiusion is realized through a local av-erageing, and all the nonlinear reaction terms are collected in a table-lookup. The special issue in t...
متن کاملInstitute for Mathematical Physics on Large Time Asymptotics for Drift{diiusion{poisson Systems on Large Time Asymptotics for Drift{diiusion{poisson Systems
In this paper we analyze the convergence rate of solutions of certain drift-diiusion-Poisson systems to their unique steady state. These bi-polar equations model the transport of two populations of charged particles and have applications for semiconductor devices and plasmas. When prescribing a connnement potential for the particles we prove exponential convergence to the equilibrium. Without c...
متن کاملFast Diffusionanduniversality near Intersecting Resonances
We study n-degree-of-freedom, nearly integrable Hamiltonian systems near the intersection of a stronger and a weaker resonance. We show the existence of motions that cross the weaker resonance faster than Arnold diiusion. We also describe families of complicated homoclinic orbits which create observable chaotic dynamics near double resonances. Quite remarkably, these families undergo a universa...
متن کاملArnold Instability for Nearly{integrable Analytic Hamiltonian Systems
A notion of instability, which is proposed as a deenition for the so{called \Arnold diiusion", for one{parameter families of nearly{integrable analytic Hamiltonian systems, is introduced. An example of unstable system is given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007