Nondensity of orbital shadowing property in C^1-topology

Mathematics – Dynamical Systems

Scientific paper

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This paper is a preliminary English translation of the corresponding paper in Russian published in Algebra and analysis, 2010,

Scientific paper

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 uses the method of skew products developed by
Yu.S. Ilyashenko and A.S. Gorodetski.

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