Nekhoroshev estimates for quasi-convex hamiltonian systems

1. Arnold, V.I. (ed.): Dynamical Systems III. (Encycl. Math. Sci., vol. 3) Berlin Heidelberg New York: Springer 1988

   Google Scholar 

2. Benettin, G., Galgani, L., Giorgilli, A.: A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems. Celestial Mech.37, 1–25 (1985)

   Article  MATH  MathSciNet  Google Scholar 

3. Benettin, G., Galgani, L., Giorgilli, A.: Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory, part II: Commun. Math. Phys.121, 557–601 (1989)

   Article  MATH  MathSciNet  Google Scholar 

4. Benettin, G., Gallavotti, G.: Stability of motions near resonances in quasi-integrable Hamiltonian systems. J. Stat. Phys.44, 293–338 (1986)

   Article  MATH  MathSciNet  Google Scholar 

5. Delshams, A., Gutiérrez, P.: Effective stability for nearly integrable Hamiltonian systems. Barcelona (Preprint 1991)

6. Fassò, F.: Lie series method for vector fields and Hamiltonian perturbation theory. J. Appl. Math. Phys.41, 843–864 (1990)

   Article  MATH  Google Scholar 

7. Gallavotti, G.: Quasi-integrable mechanical systems. In: Osterwalder, K., Stora, R. (eds.) Phénomènes critiques, systèmes aléatoires, théories de jauge, part II. Les Houches 1984, pp. 539–624. Amsterdam New York: North-Holland 1986

   Google Scholar 

8. Giorgilli, A.: New insights on the stability problem from recent results in classical perturbation theory. Università degli studi di Milano, quaderno n. 35 (Preprint 1990)

9. Giorgilli, A., Galgani, L.: Rigorous estimates for the series expansions of Hamiltonian perturbation theory. Celestial Mech.37, 95–112 (1985)

   Article  MathSciNet  Google Scholar 

10. Giorgilli, A., Zehnder, E.: Exponential stability for time dependent potentials. ETH Zürich (Preprint 1991)

11. Il'yashenko, Yu.S.: A steepness test for analytic functions. Usp. Mat. Nauk41, 193–194 (1986); Russ. Math. Surv.41, 229–230 (1986)

    MathSciNet  Google Scholar 

12. Lochak, P.: Stabilité en temps exponentiels des systèmes Hamiltoniens proches de systèmes intégrables: résonances et orbites fermés. Laboratoire Math. Ec. Norm. Supér. (Preprint 1990)

13. Lochak, P.: Canonical perturbation theory via simultaneous approximation. Ec. Norm. Supér. (Preprint 1991); Russ. Math. Surv. (to appear)

14. Lochak, P., Meunier, C.: Multiphase Averaging for Classical Systems. (Appl. Math. Sci., vol. 72) Berlin Heidelberg New York: Springer 1988

    MATH  Google Scholar 

15. Lochak, P., Neishtadt, A.I.: Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian. Chaos (to appear)

16. Molchanov, A.M.: The resonant structure of the solar system. Icarus8, 203–215 (1968)

    Article  Google Scholar 

17. Molchanov, A.M.: The reality of resonances in the solar system. Icarus11, 104–110 (1969)

    Article  Google Scholar 

18. Neishtadt, A.I.: The separation of motions in systems with rapidly rotating phase. J. Appl. Math. Mech.48(2), 133–139 (1984); Prikl. Mat. Mekh.48(2), 197–204 (1984)

    Article  MathSciNet  Google Scholar 

19. Nekhoroshev, N.N.: Behaviour of Hamiltonian systems close to integrable. Funct. Anal. Appl.5, 338–339 (1971)

    Article  MATH  Google Scholar 

20. Nekhoroshev, N.N.: An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems, I. Usp. Mat. Nauk32, 5–66, (1977); Russ. Math. Surv.32, 1–65 (1977)

    MATH  Google Scholar 

21. Nekhoroshev, N.N.: An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems, II. Tr. Semin. Petrovsk.5, 5–50 (1979); In: Oleinik, O.A. (ed.) Topics in Modern Mathematics, Petrovskii Semin, no. 5. New York: Consultant Bureau 1985

    MATH  MathSciNet  Google Scholar 

22. Pöschel, J.: Integrability of Hamiltonian systems on Cantor sets. Commun. Pure Appl. Math.35, 653–695 (1982)

    Article  MATH  Google Scholar 

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