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Diffeomorphisms on 3-manifolds with 1-dimensional basic sets which are spaciously situated on 2-torus

Y. A. Levchenko1, A. A. Shilovskaya2

AnnotationWe consider the class $G$ of diffeomorphisms satisfying Smale's Axiom $A$ on 3-manifolds, such that the nonwandering set of any diffeomorphism from $G$ belongs to the finite union of surfaces. Every surface is an embedding of torus and contains a one-dimensional spaciously situated basic set. Under certain restrictions on the structure of intersection of two-dimensional invariant manifolds of points from this basic sets, it is established the semiconjugacy of any diffeomorphism from $ G $ to a model diffeomorphism.
KeywordsA-diffeomorphism, basic set, semiconjugacy

1research associate, Nizhny Novgorod State University after N.I. Lobachevsky, Nizhny Novgorod; ulev4enko@gmail.com.

2graduate student of Nizhny Novgorod State University after N.I. Lobachevsky, Nizhny Novgorod; vesnann@mail.ru

Citation: Y. A. Levchenko, A. A. Shilovskaya, "[Diffeomorphisms on 3-manifolds with 1-dimensional basic sets which are spaciously situated on 2-torus]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,15:3 (2013) 108–111 (In Russian)