Many-dimensional solenoid invariant saddle-type sets

In the paper we construct some example of smooth diffeomorphism of closed manifold. This diffeomorphism has one-dimensional (in topological sense) basic set with stable invariant manifold of arbitrary nonzero dimension and the unstable invariant manifold of arbitrary dimension not less than two. The basic set has a saddle type, i.e. is neither attractor nor repeller. In addition, it follows from the construction that the diffeomorphism has a positive entropy and is conservative (i.e. its jacobian equals one) in some neighborhood of the one-dimensional solenoidal basic set. The construction represented in this paper allows to construct a diffeomorphism with the properties stated above on the manifold that is diffeomorphic to the prime product of the circle and the sphere of codimension one.