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Mat. Sb., 1996, Volume 187, Number 4, Pages 3–28 (Mi msb121)  

This article is cited in 14 scientific papers (total in 14 papers)

On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. II. Projectively-invariant measures

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS

Abstract: Groups of orientation-preserving homeomorphisms of $\mathbb R$ are studied. Such metric invariants as projectively-invariant measures are investigated. The approach taken results in the classification of groups of homeomorphisms by the complexity of the set of all fixed points of the group elements. In each of the classes of groups thus distinguished a finer classification is carried out in terms of the complexity of the topological structure of orbits and the combinatorial properties of the group.

DOI: https://doi.org/10.4213/sm121

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English version:
Sbornik: Mathematics, 1996, 187:4, 469–494

Bibliographic databases:

UDC: 515.168.3
MSC: Primary 54H15, 58F11; Secondary 28D05, 20F38
Received: 26.05.1993 and 22.08.1995

Citation: L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. II. Projectively-invariant measures”, Mat. Sb., 187:4 (1996), 3–28; Sb. Math., 187:4 (1996), 469–494

Citation in format AMSBIB
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II.~Projectively-invariant measures
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\yr 1996
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\pages 3--28
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    This publication is cited in the following articles:
    1. L. A. Beklaryan, “A criterion connected with the structure of the fixed-point set for the existence of a projectively invariant measure for groups of orientation-preserving homeomorphisms of $\mathbb R$”, Russian Math. Surveys, 51:3 (1996), 539–540  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. P. de la Harpe, R. I. Grigorchuk, T. Ceccherini-Silberstein, “Amenability and Paradoxical Decompositions for Pseudogroups and for Discrete Metric Spaces”, Proc. Steklov Inst. Math., 224 (1999), 57–97  mathnet  mathscinet  zmath
    3. Beklaryan, LA, “omega-projectively invariant measures for the groups of orientation-preserving homeomorpfisms of line”, Doklady Akademii Nauk, 367:6 (1999), 727  mathnet  mathscinet  zmath  isi
    4. L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$. III. $\omega$-projectively invariant measures”, Sb. Math., 190:4 (1999), 521–538  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. L. A. Beklaryan, “On a criterion for the topological conjugacy of a quasisymmetric group to a group of affine transformations of $\mathbb R$”, Sb. Math., 191:6 (2000), 809–819  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. L. A. Beklaryan, “On Analogs of the Tits Alternative for Groups of Homeomorphisms of the Circle and of the Line”, Math. Notes, 71:3 (2002), 305–315  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. L. A. Beklaryan, “Introduction to the theory of functional differential equations and their applications. Group approach”, Journal of Mathematical Sciences, 135:2 (2006), 2813–2954  mathnet  crossref  mathscinet  zmath  elib
    8. 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
    9. Bleak C., Kassabov M., Matucci F., “Structure Theorems for Groups of Homeomorphisms of the Circle”, Internat J Algebra Comput, 21:6 (2011), 1007–1036  crossref  mathscinet  zmath  isi  scopus
    10. L. A. Beklaryan, “Criteria for the Existence of an Invariant Measure for Groups of Homeomorphisms of the Line”, Math. Notes, 95:3 (2014), 304–307  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    11. 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
    12. 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
    13. 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
    14. L. A. Beklaryan, “Groups of line and circle homeomorphisms. Criteria for almost nilpotency”, Sb. Math., 210:4 (2019), 495–507  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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