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 Mat. Zametki, 2012, Volume 92, Issue 6, Pages 825–833 (Mi mz9151)

Residual Subsets in the Space of Finitely Generated Groups of Diffeomorphisms of the Circle

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS, Moscow

Abstract: Finitely generated groups of diffeomorphisms of the circle are considered in different problems of geometry, wave theory, variational calculus, etc. In particular, the set of such groups contains groups freely acting on the orbits of almost each point of the circle. The present paper deals with the structure of the set of finitely generated groups of diffeomorphisms with a given number of generators and with the above property. It is shown that such a set contains a residual subset (i.e., contains the countable intersection of open everywhere dense subsets).

Keywords: diffeomorphisms of the line, diffeomorphisms of the circle, finitely generated group, residual set, mutually transversal diffeomorphisms

DOI: https://doi.org/10.4213/mzm9151

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English version:
Mathematical Notes, 2013, 93:1, 29–35

Bibliographic databases:

UDC: 512.544.43

Citation: L. A. Beklaryan, “Residual Subsets in the Space of Finitely Generated Groups of Diffeomorphisms of the Circle”, Mat. Zametki, 92:6 (2012), 825–833; Math. Notes, 93:1 (2013), 29–35

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz9151
• https://doi.org/10.4213/mzm9151
• http://mi.mathnet.ru/eng/mz/v92/i6/p825

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. A. Beklaryan, “Groups of line and circle homeomorphisms. Metric invariants and questions of classification”, Russian Math. Surveys, 70:2 (2015), 203–248
2. Belmiloudi A., “Dynamical Behavior of Nonlinear Impulsive Abstract Partial Differential Equations on Networks With Multiple Time-Varying Delays and Mixed Boundary Conditions Involving Time-Varying Delays”, J. Dyn. Control Syst., 21:1 (2015), 95–146
3. L. A. Beklaryan, “Groups of line and circle diffeomorphisms. Criteria for almost nilpotency and structure theorems”, Sb. Math., 207:8 (2016), 1079–1099
4. L. A. Beklaryan, “Groups of line and circle homeomorphisms. Criteria for almost nilpotency”, Sb. Math., 210:4 (2019), 495–507
5. L. A. Beklaryan, “O massivnykh podmnozhestvakh v prostranstve konechno porozhdënnykh grupp diffeomorfizmov pryamoi i okruzhnosti v sluchae gladkosti $C^{(1)}$”, Fundament. i prikl. matem., 22:4 (2019), 51–74
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