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 Fundam. Prikl. Mat., 2019, Volume 22, Issue 4, Pages 51–74 (Mi fpm1816)

On massive subsets in the space of finitely generated groups of diffeomorphisms of the line and the circle in the case of $C^{(1)}$ smoothness

L. A. Beklaryan

Central Economics and Mathematics Institute Russian Academy of Sciences, Moscow

Abstract: Among the finitely generated groups of diffeomorphisms of the line and the circle, groups that act freely on the orbit of almost every point of the line (circle) are allocated. The paper is devoted to the study of the structure of the set of finitely generated groups of orientation-preserving diffeomorphisms of the line and the circle of $C^{(1)}$ smoothness with a given number of generators and the property noted above. It is shown that such a set contains a massive subset (contains a countable intersection of open everywhere dense subsets). Such a result for finitely generated groups of orientation-preserving diffeomorphisms of the circle, in the case of $C^{(2)}$ smoothness, was obtained by the author earlier.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00110_à

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Citation: L. A. Beklaryan, “On massive subsets in the space of finitely generated groups of diffeomorphisms of the line and the circle in the case of $C^{(1)}$ smoothness”, Fundam. Prikl. Mat., 22:4 (2019), 51–74

Citation in format AMSBIB
\Bibitem{Bek19} \by L.~A.~Beklaryan \paper On massive subsets in the space of finitely generated groups of diffeomorphisms of the line and the circle in the case of $C^{(1)}$ smoothness \jour Fundam. Prikl. Mat. \yr 2019 \vol 22 \issue 4 \pages 51--74 \mathnet{http://mi.mathnet.ru/fpm1816}