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Local and Global Methods of Nonlinear Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 252))

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References

  1. V. I. Arnold, “Small denominators and problems of stability of motion in classical and celestial mechanics,” Russ. Math Surv. 18, 85–193 (1963).

    Google Scholar 

  2. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, 1968).

    Google Scholar 

  3. R. B. Barrar, “Convergence of the von Zeipel procedure,” Celestial Mechanics 2, 494–504 (1970).

    Google Scholar 

  4. R. B. Barrar, “A Proof of the convergence of the Poincaré — Von Zeipel procedure in celestial mechanics, Am. J. Math. 88, 206–220 (1966).

    Google Scholar 

  5. C. E. Delaunay, Mem. Acad. Sci. Paris 28, 29 (entire volumes), 1860–1867.

    Google Scholar 

  6. D. F. Escande and F. Doveil, “Renormalization method for the onset of stochasticity in a Hamiltonian system”, Phys. Lett. 83A, 307–310 (1981).

    Google Scholar 

  7. D. F. Escande and F. Doviel, “Renormalization method for computing the threshold of the large-scale stochastic instability in two degrees of freedom Hamiltonian systems,” Stat. Phys. 26, 257–283 (1981).

    Google Scholar 

  8. H. Hagihara, Celestial Mechanics, Vol. II, Part 1 (MIT Press, 1972).

    Google Scholar 

  9. M. Hénon and C. Heiles, “The applicability of the third integral of motion: Some numerical experiments,” Astron. J. 69, 73–79 (1964).

    Google Scholar 

  10. A. N. Kolmogorov, “The conservation of conditionally periodic motions with a small change in the Hamiltonian,” Dokl. Akad. Nauk SSSR 98, 527–530 (1954).

    Google Scholar 

  11. J. Moser, “A rapidly convergent iteration method and nonlinear differential equations: II, “Ann. Scuola Norm. Sup. Pisa 20, 499–533 (1966).

    Google Scholar 

  12. J. Moser, “On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen, 1 (1962).

    Google Scholar 

  13. H. C. Plummer, An Introductory Treatise on Dynamical Astronomy (Dover, New York, 1960).

    Google Scholar 

  14. H. Poincaré, Leçons de mécanique Céleste, Vol. 1 (Gauthiers-Villars, Paris, 1905).

    Google Scholar 

  15. F. Riesz and B. Sz-Nagy, Functional Analysis (Frederick Ungar, New York, 1955).

    Google Scholar 

  16. W. M. Smart, Celestial Mechanics (Longmans, Green, New York, 1953).

    Google Scholar 

  17. Aurel Wintner, The Analytical Foundations of Celestial Mechanics (Princeton University Press, 1941).

    Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, University of Oregon, 97403, Eugene, Oregon

    Richard Barrar

Authors
  1. Richard Barrar
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A. W. Sáenz W. W. Zachary R. Cawley

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© 1984 Springer-Verlag

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Barrar, R. (1984). KAM Today. In: Sáenz, A.W., Zachary, W.W., Cawley, R. (eds) Local and Global Methods of Nonlinear Dynamics. Lecture Notes in Physics, vol 252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018327

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  • DOI: https://doi.org/10.1007/BFb0018327

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16485-2

  • Online ISBN: 978-3-540-39824-0

  • eBook Packages: Springer Book Archive

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