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Русская версия

**A. V. Osipov**

Chebyshev Laboratory,

Department of Mathematics and Mechanics,

Saint-Petersburg State University

We consider inverse periodic shadowing properties of discrete dynamical systems generated
by diffeomorphisms of closed smooth manifolds.
We show that the C^{1}-interior of the set of all diffeomorphisms
having so-called inverse periodic shadowing property coincides with the
set of Ω-stable diffeomorphisms. The equivalence of Lipschitz inverse
periodic shadowing property and hyperbolicity of
the closure of all periodic points is proved. Besides, we prove that the set
of all diffeomorphisms that have Lipschitz inverse
periodic shadowing property and whose periodic points are dense
in the nonwandering set coincides with the set of Axiom A diffeomorphisms.