Communications in Mathematical Physics

, Volume 127, Issue 2, pp 425–432 | Cite as

The system of one dimensional balls in an external field. II

  • Maciej P. Wojtkowski


We modify the system introduced in [W1] so that we can establish the nonvanishing ofall Lyapunov exponents easily.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Lyapunov Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [C-S] Chernov, N. I., Sinai, Ya. G.: Ergodic properties of some systems of 2-dimensional discs and 3-dimensional spheres. Russ. Math. Surv.42 181–207 (1987)Google Scholar
  2. [K] Katok, A.: Invariant cone families and stochastic properties of smooth dynamical systems, Preprint (1988)Google Scholar
  3. [K-S] Katok, A., Strelcyn, J.-M. with the collaboration of F. Ledrappier and F. Przytycki: Invariant manifolds, entropy and billiards; smooth maps with singularities. Lecture Notes in mathematics Vol. 1222. Berlin, Heidelberg, New York: Springer 1986Google Scholar
  4. [K-S-S] Krámli, A., Simányi, N., Szász, D.: Three billard balls on thev-dimensional torus is aK-flow. Preprint (1988)Google Scholar
  5. [W1] Wojtkowski, M. P.: A system of one dimensional balls with gravity. Commun. Math. Phys.126, 507–533 (1990)Google Scholar
  6. [W2] Wojtkowski, M. P.: Measure theoretic entropy of the system of hard spheres. Erg. Th. Dyn. Syst.8, 133–153 (1988)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Maciej P. Wojtkowski
    • 1
  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA

Personalised recommendations