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Article

О структуре одномерных базисных множеств эндоморфизмов поверхностей

Гринес В. З., Куренков Е. Д.

This paper deals with the study of the dynamics in the neighborhood of one-dimensional basic sets of Ck , k ≥ 1 , endomorphism satisfying axiom of A and given on surfaces. It is established that if one-dimensional basic set of endomorphism f has the type (1; 1) and is a onedimensional submanifold without boundary, then it is an attractor smoothly embedded in ambient surface. Moreover, there is a k ≥ 1 such that the restriction of the endomorphism fk to any connected component of the attractor is expanding endomorphism. It is also established that if the basic set of endomorphism f has the type (2; 0) and is a one-dimensional submanifold without boundary then it is a repeller and there is a k ≥ 1 such that the restriction of the endomorphism fk to any connected component of the basic set is expanding endomorphism.