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Mat. Sb., 2004, Volume 195, Number 2, Pages 17–40 (Mi msb799)  

This article is cited in 4 scientific papers (total 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.

DOI: https://doi.org/10.4213/sm799

Full text: PDF file (371 kB)
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English version:
Sbornik: Mathematics, 2004, 195:2, 163–186

Bibliographic databases:

UDC: 517.987.5
MSC: Primary 22E30; Secondary 10K05, 37A05
Received: 18.04.2003

Citation: Ya. B. Vorobets, “On the uniform distribution of orbits of finitely generated groups and semigroups of plane isometries”, Mat. Sb., 195:2 (2004), 17–40; Sb. Math., 195:2 (2004), 163–186

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gorodnik A., Maucourant F., “Proximality and equidistribution on the Furstenberg boundary”, Geom. Dedicata, 113:1 (2005), 197–213  crossref  mathscinet  zmath  isi
    2. Gorodnik A., Nevo A., “On Arnol'D'S and Kazhdan's Equidistribution Problems”, Ergod. Theory Dyn. Syst., 32:Part 6 (2012), 1972–1990  crossref  mathscinet  zmath  isi
    3. Y. Guivarc'h Jean-Pierre Conze, “Ergodicity of group actions and spectral gap, applications to random walks and Markov shifts”, DCDS-A, 33:9 (2013), 4239  crossref  mathscinet  zmath  isi
    4. Bowen L., Nevo A., “A Horospherical Ratio Ergodic Theorem For Actions of Free Groups”, Group. Geom. Dyn., 8:2 (2014), 331–353  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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