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Poisson Law for Axiom a System

In: Algorithms, Fractals, and Dynamics

Author

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  • Masaki Hirata

    (Tokyo Metropolitan University, Department of Mathematics Faculty of Sciences)

Abstract

Recently, Ya.G. Sinai studied the distribution of spacings between nearest energy levels of a quantum particle on the two-dimensional compact Riemannian surfaces, and he shows the limiting Poisson distribution for spacings of quasi-classical eigenvalues for the quantum kicked rotator model ([S.I], [S.II]) The essential point of the proof is to reduce the problem to studying some ergodic transformation on T 2. He considers the distribution of the visiting times of the trajectory to a certain horizontal strip, and obtained the limiting Poisson point process as the width of the strip tends to zero. And he points out that the way of appearance of the above Poisson point process is quite different from that in the usual situations in probability theory. This fact is very interesting from the ergodic theoretical view point. Inspired by it, we will consider the following problem.

Suggested Citation

  • Masaki Hirata, 1995. "Poisson Law for Axiom a System," Springer Books, in: Y. Takahashi (ed.), Algorithms, Fractals, and Dynamics, pages 79-87, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0321-3_6
    DOI: 10.1007/978-1-4613-0321-3_6
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