Arnold diffusion for cusp-generic nearly integrable convex systems on \({\mathbb A}^3\)

Abstract

We prove the existence of "Arnold diffusion orbits" in cusp-generic nearly integrable a priori stable systems on \({\mathbb A}^3\). The result relies on the cusp-generic existence of chains in nearly integrable a priori stable systems, proved in a previous paper, together with the existence of diffusion orbits along such chains. The latter result was obtained in collaboration with M. Gidea.