This article is cited 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.

UDC: 515.168.3

MSC: Primary 54H15, 20F38; Secondary 28D05, 30C62

Received: 16.06.1999

DOI: 10.4213/sm482

 English version: Sbornik: Mathematics, 2000, 191:6, 809–819

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