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

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

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Methods of Nonhyperbolic Shadowing

Author(s):

Sergei Yurievich Pilyugin

Dr. Sc. in Physics and Mathematics, Professor,
Faculty of Mathematics and Computer Science,
Saint Petersburg State University

sergeipil47@mail.ru

Abstract:

This paper is a survey of some recent results giving sufficient conditions of shadowing for dynamical systems in the absence of hyperbolicity. The main topics of the survey are as follows: method of pairs of Lyapunov type functions, shadowing in a neighborhood of a nonisolated fixed point, conditional multiscale shadowing for sequences of mappings of a Banach space, conditional shadowing for dynamical systems on so-called simple time scales. The paper contains a new result on conditional multiscale shadowing in the case of an infinite family of projections of the phase space.

Keywords

References:

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