L. A. Beklaryan, “On the classification of groups of orientation-preserving homeomorphisms of <nobr>$\mathbb R$</nobr>. II. Projectively-invariant measures”, Mat. Sb., 1996, Volume 187, Number 4,Pages <nobr>3

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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.

UDC: 515.168.3

MSC: Primary 54H15, 58F11; Secondary 28D05, 20F38

Received: 26.05.1993 and 22.08.1995

DOI: 10.4213/sm121