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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 8, Pages 81–86
DOI: https://doi.org/10.26907/0021-3446-2022-8-81-86
(Mi ivm9804)
 

This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

Chaotic topological foliations

N. I. Zhukova, G. S. Levin, N. S. Tonysheva

National Research University Higher School of Economics, 25/12 Bol. Pecherskaya str., Nizhny Novgorod, 603155 Russia
Full-text PDF (337 kB) Citations (3)
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Abstract: We call a foliation $(M, F)$ on a manifold $M$ chaotic if it is topologically transitive and the union of closed leaves is dense in $M$. The chaotic topological foliations of arbitrary codimension on $n$-dimensional manifold can be considered as multidimensional generalization of chaotic dynamical systems in the sense of Devaney. For topological foliations covered by fibrations we prove that a foliation is chaotic if and only if its global holonomy group is chaotic. Applying the method of suspension, a new countable family of pairwise non isomorphic chaotic topological foliations of codimension two on $3$-dimensional closed and non closed manifolds is constructed.
Keywords: foliation, chaotic foliation, suspended foliation, global holonomy group.
Funding agency Grant number
Russian Science Foundation 22-21-00304
Received: 17.06.2022
Revised: 17.06.2022
Accepted: 29.06.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 8, Pages 66–70
DOI: https://doi.org/10.3103/S1066369X22080102
Document Type: Article
UDC: 515.16
Language: Russian
Citation: N. I. Zhukova, G. S. Levin, N. S. Tonysheva, “Chaotic topological foliations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 8, 81–86; Russian Math. (Iz. VUZ), 66:8 (2022), 66–70
Citation in format AMSBIB
\Bibitem{ZhuLevTon22}
\by N.~I.~Zhukova, G.~S.~Levin, N.~S.~Tonysheva
\paper Chaotic topological foliations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 8
\pages 81--86
\mathnet{http://mi.mathnet.ru/ivm9804}
\crossref{https://doi.org/10.26907/0021-3446-2022-8-81-86}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 8
\pages 66--70
\crossref{https://doi.org/10.3103/S1066369X22080102}
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  • https://www.mathnet.ru/eng/ivm/y2022/i8/p81
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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