New Insights on the Stability problem from recent results in Classical Perturbation Theory

2.1. Periodic and quasi periodic flow 4 2.2. Isochronous and nonisochronous systems 6 2.3. A result from diophantine theory 8 2.4. The theorem of Liouville and Arnold 9 2.5. An example: the Keplerian motion 11 3. The theorem of Poincare ́ and the Arnold diffusion 14 3.1. The theorem of Poincare ́ 14 3.2. Some remarks on the theorem of Poincare ́ 16 3.3. A formally integrable case 17 3.4. The Arnold’s example of diffusion 19 4. A simple proof of the theorem of Nekhoroshev 23 4.1. Algebraic and analytic setting 23