Geodesic
Chaotic topological foliations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2022), pp. 81-86

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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.
Mots-clés : foliation
Keywords: chaotic foliation, suspended foliation, global holonomy group. 
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     author = {N. I. Zhukova and G. S. Levin and N. S. Tonysheva},
     title = {Chaotic topological foliations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {81--86},
     publisher = {mathdoc},
     number = {8},
     year = {2022},
     language = {ru},
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}
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N. I. Zhukova; G. S. Levin; N. S. Tonysheva. Chaotic topological foliations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2022), pp. 81-86. http://geodesic.mathdoc.fr/item/IVM_2022_8_a7/