Classification of the simplest non-gradient-like diffeomorphisms on 3-manifolds

The present paper is the first step in the study of Morse-Smale diffeomorphisms with heteroclinic orbits (i.e.,which are non-gradient-like)on 3-manifolds. We give a complete classification of the simplest of such diffeomorphisms.Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 7, Suzdal Conference-1, 2003.This revised version was published online in April 2005 with a corrected cover date.