An Example of Arnold Diffusion for Near-integrable Hamiltonians
نویسندگان
چکیده
In this paper, using the ideas of Bessi and Mather, we present a simple mechanical system exhibiting Arnold diffusion. This system of a particle in a small periodic potential can be also interpreted as ray propagation in a periodic optical medium with a near-constant index of refraction. Arnold diffusion in this context manifests itself as an arbitrary finite change of direction for nearly constant index of refraction.
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 کاملExistence of Diffusion Orbits in a priori Unstable Hamiltonian Systems
Under open and dense conditions we show that Arnold diffusion orbits exist in a priori unstable and time-periodic Hamiltonian systems with two degrees of freedom. 1, Introduction and Results By the KAM (Kolmogorov, Arnold and Moser) theory we know that there are many invariant tori in nearly integrable Hamiltonian systems with arbitrary n degrees of freedom. These tori are of n dimension and oc...
متن کاملFirst numerical evidence of global Arnold diffusion in quasi–integrable systems
We provide numerical evidence of global diffusion occurring in slightly perturbed integrable Hamiltonian systems and symplectic maps. We show that even if a system is sufficiently close to be integrable, global diffusion occurs on a set with peculiar topology, the so–called Arnold web, and is qualitatively different from Chirikov diffusion, occurring in more perturbed systems.
متن کاملParabolic Resonances in near Integrable Hamiltonian Systems I Introduction
When an integrable Hamiltonian system, possessing an m-resonant lower dimensional normally parabolic torus is perturbed, a parabolic m-resonance occurs. If, in addition, the iso-energetic non-degeneracy condition for the integrable system fails, the near integrable Hamiltonian exhibits a at parabolic m-resonance. It is established that most kinds of parabolic resonances are persistent in n (n 3...
متن کاملNormally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances
In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed with a small coupling between the two. This example was introduced by Arnold [1]. Using a separatrix map, introduced in a low dimensional case by Zaslavskii-Filonenko [61] and studied in a multidimensional case by Tres...
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 2008