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Break-down of stability

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Lecture Notes in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 247))

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References

  1. Aubry, S. and Le Daeron, P.Y., The discrete Frenkel-Kontorova model and its extensions I, Physica 8D, 381–422, 1983.

    ADS  Google Scholar 

  2. Birkhoff, G.D., Surface transformations and their dynamical applications, Acta Math. 43, 1–119 resp. §44, 1920.

    Google Scholar 

  3. Birkhoff, G.D., Sur quelques courbes fermées remarquables. Bull. Soc. Math. France 60, 1–26, 1932.

    MATH  MathSciNet  Google Scholar 

  4. Burkov, S.E. and Sinai, Ya.G., Non-KAM (Kolmogorov-Arnold-Moser) incommensurate states of the discrete Frenkel-Kontorova chain, Journ. Physique Lett. 45, L–409–L–412, 1984.

    Google Scholar 

  5. Hedlund, G.A., Geodesics on a two-dimensional Riemannian manifold with periodic coefficients. Am. of Math. 33, 719–739, 193

    Google Scholar 

  6. Hopf, E., Closed surfaces without conjugate points. Proc. Nct Acad. Sci. 34, 47–51, 1948.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Katok, A., Some remarks on Birkhoff and Mather twist map theorems, Ergodic Theory and Dyn. Systems 2, 185–194, 1982.

    MATH  MathSciNet  Google Scholar 

  8. Klein, A. and Ching-teh Li, Semiclassical quantization of non-separable systems. J. Math. Phys. 20, 572–578, 1979.

    Article  ADS  Google Scholar 

  9. Mather, J.N., Existence of quasi-periodic orbit orbits for twist homeomorphisms of the annulus. Topology 21, 457–467, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  10. Mather, J.N., Nonexistence of invariant circles, Ergodic theory and Dyn. Systems 4, 301–309, 1984.

    MATH  MathSciNet  Google Scholar 

  11. Morse, M., A fundamental class of geodesics on any closed surface of genus greater than one. Trans. Am. Math. Soc. 26, 25–60, 1924.

    Article  MathSciNet  MATH  Google Scholar 

  12. Moser, J., Monotone twist mappings and the calculus of variation, Preprint of the Forschungsinstitut für Mathematik, ETH, 1–22, 1985.

    Google Scholar 

  13. Percival, I.C., A variational principle for invariant tori of fixed frequency, Journ. Phys. A: Math. Gen., 12, L57–60, 1979.

    Article  ADS  MathSciNet  Google Scholar 

  14. Percival, I.C., Variational principles for invariant tori and Cantori, AIP Conference Proceedings No. 57, ed. M. Month, 1–17, 1980.

    Google Scholar 

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Authors and Affiliations

  1. Mathematik, ETH-Zentrum, Zürich, Switzerland

    Jürgen Moser

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  1. Jürgen Moser
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© 1986 Springer-Verlag Berlin Heidelberg

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Moser, J. (1986). Break-down of stability. In: Lecture Notes in Physics. Lecture Notes in Physics, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107359

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  • DOI: https://doi.org/10.1007/BFb0107359

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16455-5

  • Online ISBN: 978-3-540-39792-2

  • eBook Packages: Springer Book Archive

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