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Ergodicity of classical billiard balls

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  • Szász, Domokos

Abstract

Sinai, in 1970, proved the ergodicity of two discs on the 2-torus. Further essential progress was only reached in 1987, when Chernov and Sinai established the ergodicity of two billiard balls on the v-torus. Then, by applying a strategy suggested by Krámli, Simányi and myself in 1989, we obtained the ergodicity of three and four balls on the ν-torus (ν⩾3 in the latter case) in 1991 and 1992, while recently Simányi proved that of N balls on the ν-torus whenever ν⩾N. After a survey of this progress the study of toric billiards with cylindric scatterers is initiated and the K-property of a general class of these is claimed.

Suggested Citation

  • Szász, Domokos, 1993. "Ergodicity of classical billiard balls," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 86-92.
    • Handle: RePEc:eee:phsmap:v:194:y:1993:i:1:p:86-92
    DOI: 10.1016/0378-4371(93)90343-3
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