On embedding of arcs and circles in 3-manifolds and its application to dynamics of structurally stable 3-diffeomorhisms with two-dimensional expanding attractors

Abstract

In the present paper we prove that frames of one-dimensional separatrices in basins of sources of structurally stable 3-diffeomorhisms with two-dimensional expanding attractor are trivially embedded. This result plays an important part in the classification of such systems. The classification was given by V. Grines and E. Zhuzhoma with assumption that all one-dimensional separatrices are trivially embedded into the ambient manifold but the proof of the assumption was never given. Thus, the present paper is a necessary and nontrivial element of the classification of structurally stable diffeomorphisms with codimension one expanding attractors.