Periodic shadowing and $Ω$-stability

Details Periodic shadowing and $Ω$-stability Periodic shadowing and $Ω$-stability

2010-10-18

arxiv.org/abs/1010.3686v1

Regul. Chaotic Dyn. 15 (2010), no. 2-3, 404-417

Mathematics

Dynamical Systems

21 pages

Scientific paper

10.1134/S1560354710020255

We show that the following three properties of a diffeomorphism $f$ of a
smooth closed manifold are equivalent: (i) $f$ belongs to the $C^1$-interior of
the set of diffeomorphisms having periodic shadowing property; (ii) $f$ has
Lipschitz periodic shadowing property; (iii) $f$ is $\Omega$-stable.

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