Journal of Statistical Physics

, Volume 76, Issue 1–2, pp 587–604 | Cite as

The K-property of 4D billiards with nonorthogonal cylindric scatterers

  • Nándor Simányi
  • Domokos Szász


The K-property of cylindric billiards given on the 4-torus is established. These billiards are neither “orthogonal,” where general necessary and sufficient conditions were obtained by D. Szász, nor isomorphic to hard-ball systems, where the connecting path formula of N. Simányi is at hand.

Key Words

Local and global ergodicity hyperbolic dynamical systems semidispersing billiards cylindric billiards hard-ball systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Bunimovich, C. Liverani, A. Pellegrinotti, and Yu. Sukhov, Special systems of hard balls that are ergodic,Commun. Math. Phys. 146:357–396 (1992).CrossRefGoogle Scholar
  2. 2.
    L. A. Bunimovich and Ya. G. Sinai, On a fundamental theorem in the theory of dispersing billiards,Mat. Sbornik 90:415–431 (1973).Google Scholar
  3. 3.
    A. Krámli, N. Simányi, and D. Szász, Ergodic properties of semi-dispersing billiards I. Two cylindric scatterers in the 3-D torus,Nonlinearity 2:311–326 (1989).CrossRefGoogle Scholar
  4. 4.
    A. Krámli, N. Simányi, and D. Szász, A “transversal” fundamental theorem for semidispersing billiards,Commun. Math. Phys. 129:535–560 (1990).CrossRefGoogle Scholar
  5. 5.
    A. Krámli, N. Simányi, and D. Szász, TheK-property of three billiard balls,Ann. Math. 133:37–72 (1991).Google Scholar
  6. 6.
    A. Krámli, N. Simányi, and D. Szász, TheK-property of four billiard balls,Commun. Math. Phys. 144:107–148 (1992).CrossRefGoogle Scholar
  7. 7.
    Ya. G. Sinai, Dynamical systems with elastic reflections,Usp. Mat. Nauk 25:141–192 (1970).Google Scholar
  8. 8.
    Ya. G. Sinai, Billiard trajectories in polyhedral angle,Usp. Mat. Nauk 33:231–232 (1978).Google Scholar
  9. 9.
    N. Simányi, TheK-property ofN billiard balls I,Invent. Math. 108:521–548 (1992); II,Invent. Math. 110:151–172 (1992).CrossRefGoogle Scholar
  10. 10.
    Ya. G. Sinai and N. I. Chernov, Ergodic properties of some systems of 2-D discs and 3-D spheres,Usp. Mat. Nauk 42:153–174 (1987).Google Scholar
  11. 11.
    D. Szász, Ergodicity of classical hard balls,Physica A 194:86–92 (1993).Google Scholar
  12. 12.
    D. Szász, TheK-property of “orthogonal” cylindric billiards,Commun. Math. Phys., to appear.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Nándor Simányi
    • 1
  • Domokos Szász
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

Personalised recommendations