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Mat. Sb., 2000, Volume 191, Number 6, Pages 31–42 (Mi msb482)  

This article is cited in 6 scientific papers (total in 6 papers)

On a criterion for the topological conjugacy of a quasisymmetric group to a group of affine transformations of $\mathbb R$

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS

Abstract: A new criterion for the quasisymmetric conjugacy of an arbitrary group of orientation-preserving quasisymmetric homeomorphisms of the real line to some group of affine transformations is put forward.
In the criterion proposed by Hinkkanen one requires the uniform boundedness of constants involved in the definition of a quasisymmetric transformation over all elements of the group. In the new criterion only the uniform boundedness of constants for each cyclic subgroup is required.

DOI: https://doi.org/10.4213/sm482

Full text: PDF file (252 kB)
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English version:
Sbornik: Mathematics, 2000, 191:6, 809–819

Bibliographic databases:

UDC: 515.168.3
MSC: Primary 54H15, 20F38; Secondary 28D05, 30C62
Received: 16.06.1999

Citation: L. A. Beklaryan, “On a criterion for the topological conjugacy of a quasisymmetric group to a group of affine transformations of $\mathbb R$”, Mat. Sb., 191:6 (2000), 31–42; Sb. Math., 191:6 (2000), 809–819

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. A. Beklaryan, “Groups of homeomorphisms of the line and the circle. Topological characteristics and metric invariants”, Russian Math. Surveys, 59:4 (2004), 599–660  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. L. A. Beklaryan, “The structure of a group quasisymmetrically conjugate to a group of affine transformations of the real line”, Sb. Math., 196:10 (2005), 1403–1420  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Navas, A, “On uniformly quasisymmetric groups of circle diffeomorphisms”, Annales Academiae Scientiarum Fennicae-Mathematica, 31:2 (2006), 437  mathscinet  zmath  isi
    4. L. A. Beklaryan, “Groups of homeomorphisms of the line. Criteria for the existence of invariant and projectively invariant measures in terms of the commutator subgroup”, Sb. Math., 205:12 (2014), 1741–1760  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. L. A. Beklaryan, “Groups of line and circle homeomorphisms. Metric invariants and questions of classification”, Russian Math. Surveys, 70:2 (2015), 203–248  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    6. L. A. Beklaryan, “Groups of line and circle diffeomorphisms. Criteria for almost nilpotency and structure theorems”, Sb. Math., 207:8 (2016), 1079–1099  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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