A. Osipov

most citedPeriodic shadowing and

Ω

-stability

23 citations · 23 across the 2 of their papers we have counts for

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math.DS2011

Inverse periodic shadowing properties

Alexey V. Osipov

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…

math.DS2011

Nondensity of orbital shadowing property in C^1-topology

Alexey V. Osipov

The orbital shadowing property (OSP) of discrete dynamical systems on smooth closed manifolds is considered. Nondensity of OSP with respect to the C^1-topology is proved. The proof…

math.DS2010★ 23 cited

Periodic shadowing and $Ω$ -stability

Alexey Osipov, Sergei Yu. Pilyugin, Sergey Tikhomirov

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…

Inverse periodic shadowing properties

Nondensity of orbital shadowing property in C^1-topology

Periodic shadowing and Ω-stability

Periodic shadowing and $Ω$ -stability