Nondensity of the orbital shadowing property in 𝐶¹-topology

Osipov, A.

doi:10.1090/S1061-0022-2011-01140-9

Nondensity of the orbital shadowing property in $C^1$-topology
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by A. V. Osipov
Translated by: the author

St. Petersburg Math. J. 22 (2011), 267-292

DOI: https://doi.org/10.1090/S1061-0022-2011-01140-9

Published electronically: February 8, 2011

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Abstract:

The orbital shadowing property (OSP) of discrete dynamical systems on smooth closed manifolds is considered. The nondensity of OSP with respect to the $C^1$-topology is proved. The proof uses the method of skew products developed by Ilyashenko and Gorodetskiĭ.

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