On a criterion for the~topological conjugacy of a~quasisymmetric group to a~group of affine transformations of~$\mathbb R$
Sbornik. Mathematics, Tome 191 (2000) no. 6, pp. 809-819
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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.
@article{SM_2000_191_6_a1,
author = {L. A. Beklaryan},
title = {On a criterion for the~topological conjugacy of a~quasisymmetric group to a~group of affine transformations of~$\mathbb R$},
journal = {Sbornik. Mathematics},
pages = {809--819},
publisher = {mathdoc},
volume = {191},
number = {6},
year = {2000},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2000_191_6_a1/}
}
TY - JOUR AU - L. A. Beklaryan TI - On a criterion for the~topological conjugacy of a~quasisymmetric group to a~group of affine transformations of~$\mathbb R$ JO - Sbornik. Mathematics PY - 2000 SP - 809 EP - 819 VL - 191 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2000_191_6_a1/ LA - en ID - SM_2000_191_6_a1 ER -
%0 Journal Article %A L. A. Beklaryan %T On a criterion for the~topological conjugacy of a~quasisymmetric group to a~group of affine transformations of~$\mathbb R$ %J Sbornik. Mathematics %D 2000 %P 809-819 %V 191 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2000_191_6_a1/ %G en %F SM_2000_191_6_a1
L. A. Beklaryan. On a criterion for the~topological conjugacy of a~quasisymmetric group to a~group of affine transformations of~$\mathbb R$. Sbornik. Mathematics, Tome 191 (2000) no. 6, pp. 809-819. http://geodesic.mathdoc.fr/item/SM_2000_191_6_a1/