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Foliations of codimension one on a three-dimensional sphere with a countable family of compact attractor leaves

2017, Vol. 13, No. 4, pp.  579–584

Author(s): Zhukova N. I.

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
Citation: Zhukova N. I., Foliations of codimension one on a three-dimensional sphere with a countable family of compact attractor leaves, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 4, pp.  579–584
DOI:10.20537/nd1704010