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

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Abstract

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.

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References

  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).

    Article  Google Scholar 

  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. 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).

    Article  Google Scholar 

  4. A. Krámli, N. Simányi, and D. Szász, A “transversal” fundamental theorem for semidispersing billiards,Commun. Math. Phys. 129:535–560 (1990).

    Article  Google Scholar 

  5. A. Krámli, N. Simányi, and D. Szász, TheK-property of three billiard balls,Ann. Math. 133:37–72 (1991).

    Google Scholar 

  6. A. Krámli, N. Simányi, and D. Szász, TheK-property of four billiard balls,Commun. Math. Phys. 144:107–148 (1992).

    Article  Google Scholar 

  7. Ya. G. Sinai, Dynamical systems with elastic reflections,Usp. Mat. Nauk 25:141–192 (1970).

    Google Scholar 

  8. Ya. G. Sinai, Billiard trajectories in polyhedral angle,Usp. Mat. Nauk 33:231–232 (1978).

    Google Scholar 

  9. N. Simányi, TheK-property ofN billiard balls I,Invent. Math. 108:521–548 (1992); II,Invent. Math. 110:151–172 (1992).

    Article  Google Scholar 

  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. D. Szász, Ergodicity of classical hard balls,Physica A 194:86–92 (1993).

    Google Scholar 

  12. D. Szász, TheK-property of “orthogonal” cylindric billiards,Commun. Math. Phys., to appear.

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Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, H-1364, Budapest, Hungary

    Nándor Simányi & Domokos Szász

Authors
  1. Nándor Simányi
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  2. Domokos Szász
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This paper is dedicated to Philippe Choquard on the occasion of his 65th birthday.

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Simányi, N., Szász, D. The K-property of 4D billiards with nonorthogonal cylindric scatterers. J Stat Phys 76, 587–604 (1994). https://doi.org/10.1007/BF02188676

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  • DOI: https://doi.org/10.1007/BF02188676

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