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In this paper, we consider a class of Morse-Smale diffeomorphisms defined ona closed 3-manifold (non-necessarily orientable) under the assumption that alltheir saddle points have the same dimension of the unstable manifolds. Thesimplest example of such diffeomorphisms is the well-known ``source-sink'' or``north pole - south pole'' diffeomorphism, whose non-wandering set consists ofexactly one source and one sink. Such systems, as Reeb showed back in 1946, canbe realized only on the sphere. We generalize his result, namely, we show thatdiffeomorphisms from the considered class also can be defined only on the3-sphere.

Morse-Smale 3-diffeomorphisms with saddles of the same unstable manifold dimension