ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Inverse Periodic Shadowing Properties

Author(s):

A. V. Osipov

Chebyshev Laboratory,
Department of Mathematics and Mechanics,
Saint-Petersburg State University

osipovav@list.ru

Abstract:

We consider inverse periodic shadowing properties of discrete dynamical systems generated by diffeomorphisms of closed smooth manifolds. We show that the C1-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.

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