Numerical experiments on billiards View Full Text


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Article Info

DATE

1996-04

AUTHORS

Roberto Artuso, Giulio Casati, Italo Guarneri

ABSTRACT

We investigate decay properties of correlation functions in a class of chaotic billiards. First we consider the statistics of PoincarĂ© recurrences (induced by a partition of the billiard): the results are in agreement with theoretical bounds by Bunimovich, Sinai, and Bleher, and are consistent with a purely exponential decay of correlations out of marginality. We then turn to the analysis of the velocity-velocity correlation function: except for intermittent situations, the decay is purely exponential, and the decay rates scale in a simple way with the (uniform) curvature of the dispersing arcs. A power-law decay is instead observed when the system is equivalent to an infinite-horizon Lorentz gas. Comments are given on the behaviour of other types of correlation functions, whose decay, during the observed time scale, appears slower than exponential. More... »

PAGES

145-166

References to SciGraph publications

  • 1985-10. Numerical study of aD-dimensional periodic Lorentz gas with universal properties in JOURNAL OF STATISTICAL PHYSICS
  • 1992-10. Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2-torus in JOURNAL OF STATISTICAL PHYSICS
  • 1994-05. Periodic orbit expansions for the Lorentz gas in JOURNAL OF STATISTICAL PHYSICS
  • 1964. Monte Carlo Methods in NONE
  • 1986-08. Locating resonances for AxiomA dynamical systems in JOURNAL OF STATISTICAL PHYSICS
  • 1981-01. Statistical properties of lorentz gas with periodic configuration of scatterers in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1992-01. Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon in JOURNAL OF STATISTICAL PHYSICS
  • 1994-07. Billiards correlation functions in JOURNAL OF STATISTICAL PHYSICS
  • 1980-12. Markov Partitions for dispersed billiards in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1983-09. Power law decay of correlations in a billiard problem in JOURNAL OF STATISTICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/bf02183643

    DOI

    http://dx.doi.org/10.1007/bf02183643

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