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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
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.
Received: 17.06.2022 Revised: 17.06.2022 Accepted: 29.06.2022
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
Linking options:
https://www.mathnet.ru/eng/ivm9804 https://www.mathnet.ru/eng/ivm/y2022/i8/p81
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Abstract page: | 127 | Full-text PDF : | 35 | References: | 20 | First page: | 7 |
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