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Regular version of the site

Article

Chaos in Cartan foliations

Chaos. 2020. Vol. 30. P. 1-9.
Bazaikin Y. V., Galaev A. S., Zhukova N.

Chaotic foliations generalize Devaney's concept of chaos for
        dynamical systems. The property of a foliation to
        be chaotic is transversal. The existence problem of chaos for a Cartan foliation
        is reduced to the corresponding problem for its holonomy pseudogroup of
        local automorphisms of a transversal manifold. Chaotic foliations with transversal Cartan
        structures are investigated. 
        A Cartan $(\Phi,X)$-foliation $(M, F)$ that  admits an Ehresmann connection  is
        covered by a locally trivial bundle, and the global holonomy group of $(M, F)$
        is defined. In this case, the problem is reduced to the level of
        the global holonomy group of the foliation, which is a countable discrete subgroup of the
        Lie group of automorphisms of some simply connected Cartan $(\Phi,X)$-manifold.
        Several classes of Cartan foliations that cannot be chaotic, are indicated.
        Examples of chaotic Cartan foliations are constructed.