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  • Представление просторно расположенных совершенных аттракторов диффеоморфизмов геодезическими ламинациями

Article

Представление просторно расположенных совершенных аттракторов диффеоморфизмов геодезическими ламинациями

Гринес В. З., Куренков Е. Д.

The present paper is devoted to the topological classification of one-dimensional basiс sets of diffeomorphisms satisfying ещ the Smale's axiom A and given on orientable surfaces of negative Euler characteristic equipped with a metric of constant negative curvature. Using Lobachevsky's methods of geometry, each perfect one-dimensional attractor of A-diffeomorphism is uniquely associated with a geodesic lamination on the surface. It is established that, in the absence of special pairs of boundary periodic points in the attractor, there exists a homeomorphism of the surface homotopic to the identity that maps unstable manifolds of the points of the basic set into leaves of the geodesic lamination. Moreover, from the method of constructing geodesic laminations it follows that if the diffeomorphisms whose non-wandering sets contain perfect spaciously situated attractors are homotopic, then the geodesic laminations corresponding to these attractors coincide.