Geodesic
Foliations of codimension one on a three-dimensional sphere with a countable family of compact attractor leaves
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 4, pp. 579-584 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we present an explicit construction of a continuum family of smooth pairwise nonisomorphic foliations of codimension one on a standard three-dimensional sphere, each of which has a countable set of compact attractors which are leaves diffeomorphic to a torus. As it was proved by S.P.Novikov, every smooth foliation of codimension one on a standard three-dimensional sphere contains a Reeb component. Changing this foliation only in the Reeb component by the method presented, we get a continuum family of smooth pairwise nonisomorphic foliations containing a countable set of compact attractor leaves diffeomorphic to a torus which coincides with the original foliation outside this Reeb component.
Keywords: Reeb foliation, Reeb component, attractor of a foliation, category of foliations. 
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N. I. Zhukova. Foliations of codimension one on a three-dimensional sphere with a countable family of compact attractor leaves. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 4, pp. 579-584. http://geodesic.mathdoc.fr/item/ND_2017_13_4_a9/

[1] Novikov S. P., “Topology of foliations”, Trans. Moscow Math. Soc., 14 (1967), 268–304

[2] Tamura I., Topology of foliations: An introduction, AMS, Providence, R.I., 1992, 193 pp.