2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63599We consider a nearly integrable, non-isochronous, a-priori unstable Hamiltonian system with a (trigonometric polynomial) $O(μ)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $T_d = O((1/ μ) \log (1/ μ))$ by a variational method which does not require the existence of ``transition chains of tori'' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d$ is optimal as a consequence of a general stability result proved via classical perturbation theory.6 pagesDynamical SystemsFunctional Analysis37J40; 37J45text