Abstract
In the present paper we give a proof of Nekhoroshev's theorem, which is concerned with an exponential estimate for the stability times in nearly integrable Hamiltonian systems. At variance with the already published proof, which refers to the case of an unperturbed Hamiltonian having the generic property of steepness, we consider here the particular case of a convex unperturbed Hamiltonian. The corresponding simplification in the proof might be convenient for an introduction to the subject.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Poincaré H.: 1892, 1893, 1899,Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villars, Paris.
Kolmogorov A.N.: 1954,Dokl. Akad. Nauk. SSSR,98, N.4, 527–530;
Arnold V.I.: 1963,Russ. Math. Surveys 18, N.5, 9–36 and N.6, 85-191;
Moser J.: 1969, inProc. Int. Conf. on Functional Analysis and related topics, 60–67, University of Tokyo Press.
Poeschel J.: 1982Comm. Pure Appl. Math. 35, 653–695;
Gallavotti G.: 1983, inScaling and Self-Similarity in Physics Froelich J. (ed.), 359–426, Birkhauser, Boston.
Benettin G., Galgani L., Giorgilli A. and Strelcyn J.-M.: 1984,Nuovo Cim. 79B, 201–223.
Nekhoroshev N.N.: 1977,Russ. Math. Surveys 32 N.6, 1–65.
Nekhoroshev N.N.: 1979,Trudy Sem. Petrovs. N.5, 5–50 (in russian).
Benettin G., Galgani L. and Giorgilli A.: 1984,Nature 311, 444–446.
Glimm J.: 1964,Comm. Pure Appl. Math. 17, 509–526.
Benettin G., Galgani L. and Giorgilli A.: 1985,Nuovo Cim. 89B, 89–102;
Benettin G., Galgani L. and Giorgilli A.: 1985,Nuovo Cim. 89B, 103–119.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Benettin, G., Galgani, L. & Giorgilli, A. A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems. Celestial Mechanics 37, 1–25 (1985). https://doi.org/10.1007/BF01230338
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01230338