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 manifolds can be considered as a multidimensional generalization of chaotic dynamical systems in the Devaney sense. For topological foliations (M, F) covered by bundles, we prove that a foliation (M, F) is chaotic if and only if its global holonomy group is chaotic. Applying the method of suspension, a new countable family of pairwise nonisomorphic chaotic topological foliations of codimension two on 3-dimensional closed and nonclosed manifolds is constructed.
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Funding
This study was supported by the grant from the Russian Science Foundation, no. 22-21-00304, https://rscf.ru/project/22-21-00304.
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Translated by L. Trubitsyna
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Zhukova, N.I., Levin, G.S. & Tonysheva, N.S. Chaotic Topological Foliations. Russ Math. 66, 66–70 (2022). https://doi.org/10.3103/S1066369X22080102
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DOI: https://doi.org/10.3103/S1066369X22080102