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
I. Percival and F.Vivaldi, Physica 25D, 105 (1987)
J.H.Hannay and M.V.Berry, Physica ID, 267 (1980)
M.V.Berry, Proc.Roy.Soc.Lond. A413. 183 (1987)
V.I. Arnol’d and A.Avez, Ergodic Problems of Classical Mechanics(Benjamin, Reading, MA) (1968)
M.R. Schroeder, Number Theory in Science and Communications (Springer-Verlag) (1984)
M.Kac, Probability and Related Topics in the Physical Sciences ( Interscience, London ) (1959)
P.D.T.A. Elliott, Probablistic Number Theory Vols. 1 and 2 (New York: Springer-Verlag) (1979)
C.F.Gauss, Disquisitiones Arithmeticae (Fleisher-Liepzig) (1801)
A.Baker, A Concise Introduction to the Theory of Numbers (C.U.P.) (1984)
W.Scharlau and H.Opolka, From Fermat to Minkowski: Lectures on the Theory of Numbers and its Historical Development(New York: Springer-Verlag ) (1985)
M.Ram Murty, The Math.Intell 10. No 4, 59 (1988)
J.P.Keating, Ph.D. Thesis, University of Bristol (1989). This work will be published in more detail elsewhere.
M.Bartuccelli and F.Vivaldi, Preprint QMC DYN 88-3, (1988)
M.C.Gutzwiller, J.Math.Phys. 12, 343 (1971)
R.Balian and C.Bloch, Ann.Phys.(NY) 69, 76 (1972)
FJ.Dyson and M.L.Mehta, J.Math.Phys, 4, 701 (1963)
M.V.Berry, Proc.Roy.Soc.Lond. A400, 229 (1985)
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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
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