Ergodicity of classical billiard balls

Domokos Szász

Physica A: Statistical Mechanics and its Applications, 1993, vol. 194, issue 1, 86-92

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:194:y:1993:i:1:p:86-92

DOI: 10.1016/0378-4371(93)90343-3

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