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Funktsional'nyi Analiz i ego Prilozheniya, 2012, Volume 46, Issue 3, Pages 38–61
DOI: https://doi.org/10.4213/faa3082 (Mi faa3082) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Structure of Groups of Circle Diffeomorphisms with the Property of Fixing Nonexpandable Points

V. A. Kleptsyna, D. A. Filimonovbc

a CNRS — Unit of Mathematics, Pure and Applied
b Moscow Institute of Physics and Technology (State University)
c Moscow State University of Railway Communications
Full-text PDF (311 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa3082
Abstract: We study the structure of groups of circle diffeomorphisms with the property of fixing nonexpandable points. This property generalizes the local expansivity property, and at present there are no known examples of minimal C2 actions of finitely generated groups of circle diffeomorphisms for which this generalized property does not hold.
It turns out that if this property holds for a group action and there is at least one nonexpandable point, then the action admits a rather restrictive characterization. In particular, for such an action, we prove the existence of a Markov partition, and the structure of the action turns out to be similar to that of the Thompson group.
Keywords: dynamical system, group action, circle diffeomorphism, Markov partition.
Received: 25.06.2010
English version:
Functional Analysis and Its Applications, 2012, Volume 46, Issue 3, Pages 191–209
DOI: https://doi.org/10.1007/s10688-012-0025-1
Bibliographic databases:
Document Type: Article
UDC: 517.938.5+512.534.24
Language: Russian
Citation: V. A. Kleptsyn, D. A. Filimonov, “Structure of Groups of Circle Diffeomorphisms with the Property of Fixing Nonexpandable Points”, Funktsional. Anal. i Prilozhen., 46:3 (2012), 38–61; Funct. Anal. Appl., 46:3 (2012), 191–209
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa3082
  • https://www.mathnet.ru/eng/faa/v46/i3/p38
    • This publication is cited in the following 4 articles:
    1. Alvarez S., Filimonov D., Kleptsyn V., Malicet D., Coton C.M., Navas A., Triestino M., “Groups With Infinitely Many Ends Acting Analytically on the Circle”, J. Topol., 12:4 (2019), 1315–1367  crossref  mathscinet  zmath  isi
    2. Eskif A., Rebelo J.C., “Global Rigidity of Conjugations For Locally Non-Discrete Subgroups of Diff( )(Omega)(S-1)”, J. Mod. Dyn., 15 (2019), 41–93  crossref  mathscinet  zmath  isi
    3. Deroin B., Kleptsyn V., Navas A., “On the Ergodic Theory of Free Group Actions By Real-Analytic Circle Diffeomorphisms”, Invent. Math., 212:3 (2018), 731–779  crossref  mathscinet  zmath  isi  scopus
    4. D. A. Filimonov, V. A. Kleptsyn, “One-end finitely presented groups acting on the circle”, Nonlinearity, 27:6 (2014), 1205–1223  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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