ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Weak Shadowing Property in Omega-Stable Diffeomorphisms


O. A. Tarakanov

St. Petersburg State University,
Department of Mathematics and Mechanics,
University av., 28, 198504, St. Petersburg, RUSSIA,


The weak shadowing property was introduced by R.M. Corless and S.Yu. Pilyugin and studied by these authors, K. Sakai, O.B. Plamenevskaya and others. It was shown by Plamenevskaya that for omega-stable diffeomorphisms this property may be bount to the numerical properties of the eigenvalues of the hyperbolic saddle points of the diffeomorphisms.
In this paper, we prove that if the phase diagram of an omega-stable diffeomorphism of a manifold does not contain chains of length more than three, then it has the weak shadowing property.

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