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Semiclassical Properties of the Cat Maps

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Number Theory and Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 47))

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Abstract

The cat maps are a family of completely chaotic Hamiltonian dynamical systems whose classical and quantum mechanics are especially well understood.

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References

  1. I. Percival and F.Vivaldi, Physica 25D, 105 (1987)

    MathSciNet  MATH  Google Scholar 

  2. J.H.Hannay and M.V.Berry, Physica ID, 267 (1980)

    Google Scholar 

  3. M.V.Berry, Proc.Roy.Soc.Lond. A413. 183 (1987)

    Article  ADS  Google Scholar 

  4. V.I. Arnol’d and A.Avez, Ergodic Problems of Classical Mechanics(Benjamin, Reading, MA) (1968)

    Google Scholar 

  5. M.R. Schroeder, Number Theory in Science and Communications (Springer-Verlag) (1984)

    Google Scholar 

  6. M.Kac, Probability and Related Topics in the Physical Sciences ( Interscience, London ) (1959)

    Google Scholar 

  7. P.D.T.A. Elliott, Probablistic Number Theory Vols. 1 and 2 (New York: Springer-Verlag) (1979)

    Google Scholar 

  8. C.F.Gauss, Disquisitiones Arithmeticae (Fleisher-Liepzig) (1801)

    Google Scholar 

  9. A.Baker, A Concise Introduction to the Theory of Numbers (C.U.P.) (1984)

    Google Scholar 

  10. W.Scharlau and H.Opolka, From Fermat to Minkowski: Lectures on the Theory of Numbers and its Historical Development(New York: Springer-Verlag ) (1985)

    MATH  Google Scholar 

  11. M.Ram Murty, The Math.Intell 10. No 4, 59 (1988)

    Google Scholar 

  12. J.P.Keating, Ph.D. Thesis, University of Bristol (1989). This work will be published in more detail elsewhere.

    Google Scholar 

  13. M.Bartuccelli and F.Vivaldi, Preprint QMC DYN 88-3, (1988)

    Google Scholar 

  14. M.C.Gutzwiller, J.Math.Phys. 12, 343 (1971)

    Article  ADS  Google Scholar 

  15. R.Balian and C.Bloch, Ann.Phys.(NY) 69, 76 (1972)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. FJ.Dyson and M.L.Mehta, J.Math.Phys, 4, 701 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. M.V.Berry, Proc.Roy.Soc.Lond. A400, 229 (1985)

    Article  ADS  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK

    J. P. Keating

Authors
  1. J. P. Keating
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Editor information

Editors and Affiliations

  1. Service de Physique Théorique, C.E.N Saclay, F-91191, Gif-sur-Yvette Cedex, France

    Jean-Marc Luck  & Pierre Moussa  & 

  2. Institut Henri-Poincaré, Problèmes Diophantiens, Université de Paris 6, F-75231, Paris Cedex 05, France

    Michel Waldschmidt

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© 1990 Springer-Verlag Berlin Heidelberg

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Keating, J.P. (1990). Semiclassical Properties of the Cat Maps. In: Luck, JM., Moussa, P., Waldschmidt, M. (eds) Number Theory and Physics. Springer Proceedings in Physics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75405-0_32

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  • DOI: https://doi.org/10.1007/978-3-642-75405-0_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-75407-4

  • Online ISBN: 978-3-642-75405-0

  • eBook Packages: Springer Book Archive

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