Inverse periodic shadowing properties

Details Inverse periodic shadowing properties Inverse periodic shadowing properties

2011-03-29

arxiv.org/abs/1103.5608v1

Mathematics

Dynamical Systems

15 pages, a preprint

Scientific paper

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 $\Omega$-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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