Abstract:
Groups of orientation-preserving homeomorphisms of R are studied. Such metric invariants as invariant and 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.
Citation:
L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of R.
I. Invariant measures”, Sb. Math., 187:3 (1996), 335–364
\Bibitem{Bek96}
\by L.~A.~Beklaryan
\paper On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$.
I.~Invariant measures
\jour Sb. Math.
\yr 1996
\vol 187
\issue 3
\pages 335--364
\mathnet{http://mi.mathnet.ru/eng/sm115}
\crossref{https://doi.org/10.1070/SM1996v187n03ABEH000115}
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\zmath{https://zbmath.org/?q=an:0870.54040}
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This publication is cited in the following 14 articles:
L. A. Beklaryan, “Groups of line and circle diffeomorphisms. Criteria for almost nilpotency and structure theorems”, Sb. Math., 207:8 (2016), 1079–1099
L. A. Beklaryan, “Groups of line and circle homeomorphisms. Metric invariants and questions of classification”, Russian Math. Surveys, 70:2 (2015), 203–248
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
Bleak C., Kassabov M., Matucci F., “Structure Theorems for Groups of Homeomorphisms of the Circle”, Internat J Algebra Comput, 21:6 (2011), 1007–1036
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
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
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
Linnell, PA, “Left ordered groups with no non-abelian free subgroups”, Journal of Group Theory, 4:2 (2001), 153
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
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
Beklaryan, LA, “omega-projectively invariant measures for the groups of orientation-preserving homeomorpfisms of line”, Doklady Akademii Nauk, 367:6 (1999), 727
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
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
L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of $\mathbb R$.
II. Projectively-invariant measures”, Sb. Math., 187:4 (1996), 469–494
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