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In this paper, we study the structural stability of three-dimensionaldiffeomorphisms with source-sink dynamics. Here the role of source and sink isplayed by one-dimensional hyperbolic repeller and attractor. It is well knownthat in the case when the repeller and the attractor are solenoids (notembedded in the surface), the diffeomorphism is not structurally stable. Theauthor proves that in the case when the attractor and the repeller arecanonically embedded in a surface, the diffeomorphism is also not structurallystable.

There are no structural stable Axiom A 3-diffeomorphisms with dynamics "one-dimensional surfaced attractor-repeller"