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Article

О топологической классификации диффеоморфизмов на 3-многообразиях с поверхностными двумерными аттракторами и репеллерами

Нелинейная динамика. 2014. Т. 10. № 1. С. 17-33.

Consider the class of diffeomorphisms of three-dimensional manifolds and satisfying aksiomA by Smale on the assumption that the non-wandering set of each diffeomorphism consists of surface two-dimensional basic sets. We find interrelations between the dynamics of such a diffeomorphism and the topology of the ambient manifold. Also found that each such diffeomorphism is Ω-conjugate to a modeling diffeomorphism of the manifold, which is a locally trivial bundle over the circle with torus as a leaf. Under some restrictions on the asymptotic behavior of two-dimensional invariant manifolds of points of basis sets obtained the topological classification of structurally stable diffeomorphisms of the class.