منابع مشابه
Dynamics of the dominant Hamiltonian, with applications to Arnold diffusion
It is well know that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associated averaged system, called slow system. Each resonance is defined by a basis (a collection of integer vectors). We introduce a class of resonances whose basis can be divided into two well separated groups and call them...
متن کاملGeometry of Arnold Diffusion
The goal of this paper is to present to non-specialists what is perhaps the simple possible geometrical picture explaining the mechanism of Arnold diffusion. We choose to speak of a specific model – that of geometric rays in a periodic optical medium. This model is equivalent to that of a particle in a periodic potential in R with energy prescribed and to the geodesic flow in a Riemannian metri...
متن کاملChaos and Arnold Diffusion in Dynamical Systems
Abs~act -Chaotic motion refers to complicated trajectories in dynamical systems. It occurs even in deterministic systems governed by simple differential equations and its presence has been experimentally verified for many systems in several disciplines.-A technique-due to Melnikov provides an analytical tool for measuring chaos caused by horseshoes in certain systems.. The .phenomenon .of .,Amo...
متن کاملArnold Diffusion: a Functional Analysis Approach
Topological instability of action variables in multidimensional nearly integrable Hamiltonian systems is known as Arnold diffusion. This phenomenon was pointed out in 1964 by Arnold himself in his famous paper [3]. For autonomous Hamiltonian systems with two degrees of freedom KAM theory generically implies topological stability of the action variables (i.e. the time-evolution of the action var...
متن کاملStochastic dynamics and control of a driven nonlinear spin chain: the role of Arnold diffusion.
We study a chain of nonlinear interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical calculations show the possibility of stochastic control if the underlying semiclassical dynamics is chaotic. This is achievable by tuning the external field parameters...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2003
ISSN: 0022-0396
DOI: 10.1016/s0022-0396(02)00053-0