Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T18:31:28.536Z Has data issue: false hasContentIssue false
  • English
  • Français

Perturbed billiard systems, I. The ergodicity of the motion of a particle in a compound central field

Published online by Cambridge University Press:  22 January 2016

I. Kubo
I. Kubo*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

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.

The ergodicity of classical dynamical systems which appear really in the statistical mechanics was discussed by Ya. G. Sinai [9]. He announced that the dynamical system of particles with central potential of special type in a rectangular box is ergodic. However no proofs have been given yet. Sinai [11] has given a proof of the ergodicity of a simple one-particle model which is called a Sinai billiard system.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 61 , July 1976 , pp. 1 - 57
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Ambrose, W. and Kakutani, S.: Structure and continuity of measurable flow. Duke Math. J. 9 (1942), 25–42.Google Scholar
[2] Bunimovich, L. A. and Sinai, Ya. G.: On a fundamental theorem in the theory of dispersing billiards, Math. USSR-Sb. 90 (1973), 407–423.Google Scholar
[3] Gallavotti, G. and Ornstein, D. S.: Billiards and Bernouilli schemes, (preprint).Google Scholar
[4] Kakutani, S.: Induced measure preserving transformations, Proc. Imp. Acad., Tokyo 19 (1943), 625–641.Google Scholar
[5] Kubo, L.: Quasi-flows, Nagoya Math. J. 35 (1969), 1–30.CrossRefGoogle Scholar
[6] Kubo, I.: Billiard systems, Lecture Notes (preparing).Google Scholar
[7] Kubo, I. and Murata, H.: Perturbed Billiard systems II (preparing).Google Scholar
[8] Rohlin, V. I. and Sinai, Ya. G.: Construction and properties of invariant measurable partitions, Dokl. Akad. Nauk 4, No. 5 (1961), 1034–1041.Google Scholar
[9] Sinai, Ya. G.: On the foundations of the ergodic hypothesis for a dynamical system of statistical mechanics, Soc. Math. Dokl. 4, No. 6 (1963), 1818–1822.Google Scholar
[10] Sinai, Ya. G.: Classical dynamical systems with countably multiple Lebesgue spectra II, A. M. S. Transl. (2) 68 (1968), 34–68.Google Scholar
[11] Sinai, Ya. G.: Dynamical systems with elastic reflections, Russian Math. Surveys 25 (1970), 137–189.Google Scholar