An Exponential Estimate of the Time of Stability of Nearly-Integrable Hamiltonian Systems

CONTENTS § 1. Introduction § 2. Unsolved problems. Conjectures. Generalizations § 3. The main ideas of the proof of the exponential estimate § 4. Steepness conditions. Precise statement of the main theorem § 5. Forbidden motions § 6. Resonances. Resonance zones and blocks § 7. Dependence of the diameters of the discs of fast drift on the steepness of the unperturbed Hamiltonian § 8. Condition for the non-overlapping of resonances § 9. Traps in frequency systems. Completion of the proof of the main theorem § 10. Statement of the lemma on the elimination of non-resonance harmonics, and of the technical lemmas used in the proof of the main theorem § 11. Remarks on the proof of the main theorem § 12. Application of the main theorem to the many-body problem References