Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T03:09:09.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-particle billiard system with arbitrary mass ratio

Published online by Cambridge University Press:  19 September 2008

Nándor Simányi  and
Maciej P. Wojtkowski
Nándor Simányi
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest 1364, P.O. Box 127, Hungary
Maciej P. Wojtkowski
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe ergodic properties of the system of two hard discs with arbitrary masses moving on the two dimensional torus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 1 , March 1989 , pp. 165 - 171
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[Bun-Sin]Bunimovich, L. A. & Sinai, Ya G.. On a fundamental theorem in the theory of dispersing billiards. Math. USSR Sbomik 19 (1973), 407–423.CrossRefGoogle Scholar
[Gal]Gallavotti, G.. Lectures on billiards. Lecture Notes in Physics 38 (Springer: Berlin-New York, 1975).Google Scholar
[Gal-Orn]Gallavotti, G. & Ornstein, D. S.. Billiards and Bernoulli schemes. Comm. Math. Phys. 38 (1974), 83–101.CrossRefGoogle Scholar
[Kel]Keller, G.. Diplomarbeit. Erlangen (1977).Google Scholar
[Kub]Kubo, I.. Perturbed billiard systems I. The ergodicity of the motion of a particle in a compound central field. Nagoya Math. J. 61 (1976), 1–57.CrossRefGoogle Scholar
[Kub-Mur]Kubo, I. & Murata, H.. Perturbed billiard systems II. Bernoulli properties. Nagoya Math. J. 81 (1981), 1–25.CrossRefGoogle Scholar
[Rud]Rudolph, D. J.. Classifying the isometric extensions of a Bernoulli shift. J. d'Anal Math. 34 (1978), 36–50.CrossRefGoogle Scholar
[Sin1]Sinai, Ya. G.. Dynamical systems with elastic reflections. Russian Math. Surveys 25 (1970), 137–189.CrossRefGoogle Scholar
[Sin2]Sinai, Ya. G.. Dynamical systems with countably multiple Lebesgue spectrum II. Amer. Math. Soc. Transl. 68(2) (1968), 34–38.Google Scholar