Arnold diffusion in large systems

Chaos 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...

Arnold diffusion in perturbations of analytic integrable Hamiltonian systems

Arnold diffusion in Hamiltonian Systems 1: a priori Unstable Case

By using variational method and under generic conditions we show that Arnold diffusion exists in a priori unstable and time-periodic Hamiltonian systems with multiple degrees of freedom.

Geometry 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...

Horseshoes and Arnold Diffusion for Hamiltonian Systems on Lie Groups

This paper presents theorems which establish the existence of horseshoes and Arnold diffusion for nearly integrable Hamiltonian systems associated with Lie groups. The methods are based on our two previous papers, Holmes and Marsden [1982a], [1982b). The two main examples treated here are as follows: 1. A simplified model of the rigid body with attachments. This system has horseshoes (with one ...