A. V. Osipov, “Nondensity of the orbital shadowing property in <nobr>$C^1$</nobr>-topology”, Algebra i Analiz, 2010, Volume 22, Issue 2,Pages <nobr>127

This article is cited in 6 papers

Research Papers

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

A. V. Osipov

St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

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.

Keywords: shadowing, generic property, skew product, $C^1$-topology.

Received: 28.02.2009