Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2000},
     volume = {191},
     number = {6},
     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
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
%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/

[1] Alfors L. V., Lektsii po kvazikonformnym otobrazheniyam, Mir, M., 1969 | MR

[2] Hinkkanen A., “The structure of certain quasisymmetrik groups”, Mem. Amer. Math. Soc., 83:422 (1990), 1–87 | MR

[3] Beklaryan L. A., “K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu. I: Invariantnye mery”, Matem. sb., 187:3 (1996), 23–54 | MR | Zbl

[4] Beklaryan L. A., “K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu. II: Proektivno-invariantnye mery”, Matem. sb., 187:4 (1996), 3–28 | MR | Zbl

[5] Kornfeld I. P., Sinai Ya. G., Fomin S. V., Ergodicheskaya teoriya, Nauka, M., 1980 | MR | Zbl

[6] Beklaryan L. A., “Kriterii suschestvovaniya proektivno-invariantnoi mery dlya grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu, svyazannyi so strukturoi mnozhestva nepodvizhnykh tochek”, UMN, 51:3 (1996), 179–180 | MR | Zbl

[7] Beklaryan L. A., “K voprosu o klassifikatsii grupp gomeomorfizmov $\mathbb R$, sokhranyayuschikh orientatsiyu. III: $\omega$-proektivno-invariantnye mery”, Matem. sb., 190:4 (1999), 43–62 | MR | Zbl