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K for KAM

Kolmogorov–Arnold–Moser

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Lettera Matematica

Abstract

The aim of this paper is to introduce the main aspects of the KAM theorem, in particular its relevance in celestial mechanics and statistical mechanics.

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References

  1. Castiglione, P., Falcioni, M., Lesne, A., Vulpiani, A.: Chaos and Coarse Graining in Statistical Mechanics. Cambridge University Press, Cambridge (2008)

    Book  MATH  Google Scholar 

  2. Charpentier, E., Lesne, A., Nikolski, N.K., (eds.): Kolmogorov’s heritage in mathematics Springer, Berlin (2007)

  3. Charpentier, R., Ghys, E., Lesne, A. (eds.): The Scientific Legacy of Poincaré. American Mathematical Society, Providence (2010)

    MATH  Google Scholar 

  4. Contopoulos, G.: Order and Chaos in Dynamical Astronomy. Springer, Berlin (2010)

    MATH  Google Scholar 

  5. Dumas, H.S.: The KAM Story. World Scientific, Singapore (2014)

    Book  MATH  Google Scholar 

  6. Fermi, E., Pasta, J.R., Ulam, S.: Studies of nonlinear problems. Report LA-1940. Los Alamos Scientific Laboratory, Los Alamos (1955)

  7. Gallavotti, G. (ed.): The Fermi-Pasta-Ulam Problem: A Status Report. Springer, Berlin (2007)

    MATH  Google Scholar 

  8. Hénon, M., Heiles, C.: The applicability of the third integral of motion: some numerical experiments. Astron. J. 69, 73–79 (1964)

    Article  MathSciNet  Google Scholar 

  9. Leibniz, G.W.: Mr. Leibnitz’s First Paper. In: Clarke, S.: A Collection of Papers, Which passed between the late Learned Mr. Leibnitz, and Dr. Clarke, In the Years 1715 and 1716, London (1717). http://www.newtonproject.ox.ac.uk/view/texts/normalized/THEM00226

  10. Livi, R., Vulpiani, A. (eds.): The Kolmogorov Legacy in Physics. Springer, Berlin (2003)

    MATH  Google Scholar 

  11. MacKay, R.S., Meiss, J.D. (eds.): Hamiltonian Dynamical Systems: A Reprint Selection. CRC, Boca Raton (1987)

    MATH  Google Scholar 

  12. Morbidelli, A.: Modern Celestial Mechanics: Aspects of Solar System Dynamics. Taylor & Francis, London (2002)

    Google Scholar 

  13. Verhulst, F.: Henri Poincaré: Impatient Genius. Springer, Berlin (2012)

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Angelo Vulpiani

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  1. Angelo Vulpiani
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Correspondence to Angelo Vulpiani.

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Vulpiani, A. K for KAM. Lett Mat Int 5, 137–141 (2017). https://doi.org/10.1007/s40329-017-0173-5

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  • DOI: https://doi.org/10.1007/s40329-017-0173-5

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