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Intrinsic nonadiabaticities on the Farey tree

  • I. Dana
  • W. P. Reinhardt
B. Quantum Chaos
Part of the Lecture Notes in Physics book series (LNP, volume 278)

Keywords

Rational Number Boundary Circle Adiabatic Invariance Island Chain Small Denominator 
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.
    I. Dana and W. P. Reinhardt, “Adiabatic Invariance in the Standard Map”, University of Pennsylvania preprint, to be published.Google Scholar
  2. 2.
    E. A. Solovev, Sov. Phys.-JETP 48, 635 (1978); T. P. Grozdanov and E. A. Solovev, J. Phys. B 15, 1195 (19.82); B. R. Johnson, J. Chem. Phys. 83, 1204 (1985); R. T. Skodje, F. Borondo, and W. P. Reinhardt, J. Chem. Phys. 82, 4611 (1985); R. T. Skodje and F. Borondo, Chem. Phys. Lett. 118, 409 (1985); C. W. Patterson, J. Chem. Phys. 83, 4618 (1985); T. P. Grozdanov, S. Saini, and H. S. Taylor, Phys. Rev. A 33, 55 (1986); J. W. Zwanziger, E. R. Grant, and G. S. Ezra, to be published.ADSGoogle Scholar
  3. 3.
    P. A. M. Dirac, Proc. R. Soc. 107, 725 (1925).ADSCrossRefGoogle Scholar
  4. 4.
    J. L. Tennyson, J. R. Cary, and D. F. Escande, Phys. Rev. Lett. 56, 2117 (1986), and to be published.Google Scholar
  5. 5.
    B. V. Chirikov, Phys. Rep. 52, 263 (1979), and references therein.ADSCrossRefGoogle Scholar
  6. 6.
    J. M. Greene, J. Math. Phys. 20, 1183 (1979).ADSCrossRefGoogle Scholar
  7. 7.
    M. V. Berry, N. L. Balasz, M. Tabor, and A. Voros, Ann. Phys. (N.Y.) 122, 26 (1979).ADSCrossRefGoogle Scholar
  8. 8.
    See, e.g., R. S. Mackay, J. D. Meiss, and I. C. Percival, “Resonances in Area-Preserving Maps”, preprint QMC DYN 86.4, submitted to Physica D. Some of the terms related to the Farey tree in this work have been used by us.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • I. Dana
    • 1
  • W. P. Reinhardt
    • 1
  1. 1.Department of Chemistry and the Laboratory for Research on the Structure of MatterUniversity of PennsylvaniaPhiladelphiaUSA

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