Inverse periodic shadowing properties

zbMATH Open1412.37033arXiv1103.5608MaRDI QIDQ3121658

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Publication date: 20 March 2019

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1103.5608

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