Geodesic
Nondensity of the orbital shadowing property in $C^1$-topology
Algebra i analiz, Tome 22 (2010) no. 2, pp. 127-163.

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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.
Keywords: shadowing, generic property, skew product, $C^1$-topology. 
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A. V. Osipov. Nondensity of the orbital shadowing property in $C^1$-topology. Algebra i analiz, Tome 22 (2010) no. 2, pp. 127-163. http://geodesic.mathdoc.fr/item/AA_2010_22_2_a3/

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