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Subharmonics and the transition to chaos

  • Joseph Rudnick
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 179)

Keywords

Recursion Relation Period Doubling Driving Frequency Edge Wave Symbol String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    M. Faraday, Philos. Trans. Roy. Soc. London 299, Sec. 103 (1831).Google Scholar
  2. 2.
    C. Hayashi, Nonlinear Oscillations in Physical Systems (McGraw-Hill, New York, 1964).Google Scholar
  3. 3.
    A.B. Pippard, The Physics of Vibration (Cambridge Univ. Press, Cambridge, 1978) Vol 1, Chap. 9.Google Scholar
  4. 4.
    M. Feigenbaum, J. Stat. Phys. 19, 25 (1978) and 21, 669 (1979).CrossRefGoogle Scholar
  5. 5.
    M. Gorman and H.L. Swinney, Phys. Rev. Lett. 43, 1871 (1979).Google Scholar
  6. 6.
    J.P. Gollub, S.V. Benson and J. Steinman, Ann. N.Y. Acad. Sci. 357, 22 (1980).Google Scholar
  7. 7.
    A. Libchaber and J. Maurer, J. Phys. (Paris), Colloq. 41, C3–51 (1980).Google Scholar
  8. 8.
    M. Giglio, S. Musazzi and V. Perini, Phys. Rev. Lett. 47, 243 (1981).Google Scholar
  9. 9.
    R. Keolian, L.A. Turkevich, S.J. Putterman, I. Rudnick and J. Rudnick, Phys. Rev. Lett. 47, 1133 (1981).Google Scholar
  10. 10.
    M. Nauenberg and J. Rudnick, Phys. Rev. B24, 493 (1981).Google Scholar
  11. 11.
    N.W. Ashcroft and N.D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).Google Scholar
  12. 12.
    A.I. Khinchin, Continued Fractions (Noordhoff, 1963).Google Scholar
  13. 13.
    P. Manneville and Y. Pomeau, Phys. Lett. 75A, (1979) and Physica 1D, 219 (1980); Y Pomeau and P. Manneville, Commun. Math. Phys. 74, 189 (1980).Google Scholar
  14. 14.
    J.E. Hirsch, B.A. Huberman and D.J. Scalapino, Phys. Rev. A25, 519 (1982).Google Scholar
  15. 15.
    J.E. Hirsch, M. Nauenberg and D.J. Scalapino, Phys. Lett. 87A, 391 (1982).Google Scholar
  16. 16.
    B. Hu and J. Rudnick, Phys. Rev. Lett. 48, 1645 (1982).Google Scholar
  17. 17.
    Eckart, C. Wave Rep. 100, Scripps Inst. of Oceanogr. Univ. of Calif., La Jolla (1951).Google Scholar
  18. 18.
    Ursell, F. Proc. Roy. Soc. London, Ser. A, 214, 79 (1952).Google Scholar
  19. 19.
    R.T. Guza and R.E. Davis, J. Geophys. Research, 79, 1285 (1974).Google Scholar
  20. 20.
    D. Rudnick, private communication.Google Scholar
  21. 21.
    M.J. Feigenbaum, Phys. Lett. 74A, 375 (1979); Commun. Math. Phys. 77, 65 (1980).Google Scholar
  22. 22.
    Filling in the steps here is left as a challenging, but not overwhelming, excercise.Google Scholar
  23. 23.
    P. Collet, J.-P. Eckmann and L. Thomas, Commun, Math. Phys. 81, 261 (1981).Google Scholar
  24. 24.
    B.A. Huberman and J. Rudnick, Phys. Rev. Lett. 45, 154 (1980).Google Scholar
  25. 25.
    See, also, the “Amateur Scientist” section of Scientific American, 247 (1982).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Joseph Rudnick
    • 1
  1. 1.Physics DepartmentUniversity of CaliforniaSanta CruzUSA

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