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

TL;DR

This paper proves the existence of Arnold diffusion orbits in cusp-generic nearly integrable convex systems on a three-dimensional annulus, advancing understanding of instability mechanisms in Hamiltonian dynamics.

Contribution

It establishes the existence of diffusion orbits along chains in cusp-generic systems, building on prior work on chain existence and diffusion mechanisms.

Findings

Existence of Arnold diffusion orbits in cusp-generic systems.

Chains in nearly integrable systems are proven to facilitate diffusion.

Diffusion orbits are constructed along these chains.

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.