## On hyperbolic attractors and repellers of endomorphisms. (arXiv:1711.03338v1 [math.DS])

It is well known that topological classification of dynamical systems with
hyperbolic dynamics is significantly defined by dynamics on nonwandering set.
F. Przytycki generalized axiom $A$ for smooth endomorphisms that was previously
introduced by S. Smale for diffeomorphisms and proved spectral decomposition
theorem which claims that nonwandering set of an $A$-endomorphism is a union of
a finite number basic sets. In present paper the criterion for a basic sets of
an $A$-endomorphism to be an attractor is given. Moreover, dynamics on basic
sets of codimension one is studied. It is shown, that if an attractor is a
topological submanifold of codimension one of type $(n-1, 1)$, then it is
smoothly embedded in ambient manifold and restriction of the endomorphism to
this basic set is an expanding endomorphism. If a basic set of type $(n, 0)$ is
a topological submanifold of codimension one, then it is a repeller and
restriction of the endomorphism to this basic set is also an expanding
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