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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Nondensity of the orbital shadowing property in $ C^1$-topology


Author: A. V. Osipov
Translated by: the author
Original publication: Algebra i Analiz, tom 22 (2010), nomer 2.
Journal: St. Petersburg Math. J. 22 (2011), 267-292
MSC (2010): Primary 37C50
Published electronically: February 8, 2011
MathSciNet review: 2668126
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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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Additional Information

A. V. Osipov
Affiliation: Mathematics and Mechanics Department, St. Petersburg State University, 28 Universitetskiĭ Prospekt, Staryĭ Peterhof, St. Petersburg 198504, Russia
Email: osipovav@list.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01140-9
PII: S 1061-0022(2011)01140-9
Keywords: Shadowing, generic property, skew product, $C^{1}$-topology
Received by editor(s): February 28, 2009
Published electronically: February 8, 2011
Article copyright: © Copyright 2011 American Mathematical Society