In Middle Volga Mathematical Society

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

Yu. A. Levchenko, A. A. Shilovskaya

Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: We 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.

Keywords: A-diffeomorphism, basic set, semiconjugacy.

UDC: 517.9