This article is cited in 2 papers

Groups of line and circle diffeomorphisms. Criteria for almost nilpotency and structure theorems

L. A. Beklaryan<sup>ab

a</sup> Peoples Friendship University of Russia, Moscow
^b Central Economics and Mathematics Institute Russian Academy of Sciences, Moscow

Abstract: Almost nilpotency criteria and structure theorems are presented for the class of finitely generated groups of line and circle diffeomorphisms with mutually transversal elements. Key ingredients in the proof of the structure theorems are the existence/absence of an invariant measure, the (previously established) criterion for the existence of an invariant measure and restatements of this criterion in terms of various (topological, algebraic, combinatorial) characteristics of the group. The question of whether certain features of these characteristics or the existence of an invariant measure are typical for groups of line and circle diffeomorphisms is discussed.
Bibliography: 34 titles.

Keywords: groups of diffeomorphisms, almost nilpotency criterion, invariant measure.

UDC: 512.544.43

MSC: 37E05, 37E10, 57M60

Received: 05.09.2015 and 18.01.2016

DOI: 10.4213/sm8596

 English version: Sbornik: Mathematics, 2016, 207:8, 1079–1099

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