Geometry of Arnold diffusion

The goal of this paper is to present to nonspecialists what is perhaps the simplest 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 ℝⁿ with energy prescribed and to the geodesic flow in a Riemannian metric on ℝⁿ.