This article is cited in 4 papers

On the uniform distribution of orbits of finitely generated groups and semigroups of plane isometries

Ya. B. Vorobets

Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine

Abstract: Actions by isometries on a Euclidean plane of free groups and free semigroups with arbitrarily many generators and of free products of groups of order 2 are considered. It is shown that, in the typical case, all orbits of the action are uniformly distributed in the plane. The actions for which the distribution of orbits fails to be uniform are explicitly described.

UDC: 517.987.5

MSC: Primary 22E30; Secondary 10K05, 37A05

Received: 18.04.2003

DOI: 10.4213/sm799

 English version: Sbornik: Mathematics, 2004, 195:2, 163–186

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