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Methods of Nonhyperbolic Shadowing

Автор(ы):

Sergei Yurievich Pilyugin

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

sergeipil47@mail.ru

Аннотация:

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.

Ключевые слова

Ссылки:

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  2. Palmer K. [Shadowing in Dynamical Systems. Theory andApplications], Dordrecht, Kluwer Acad. Publ., 2000. XIV+299 p
  3. Pilyugin S. Yu., Sakai K. [Shadowing and Hyperbolicity]. Lect. Notes Math., Vol. 2193, Cham, Springer Intern. Publ., 2017. XIV+216 p
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  9. Lewowicz J., [Lyapunov functions and topological stability]. J. Differ. Equat. , 1980, Vol. 38, 192-209
  10. Pilyugin S. Yu. [Perturbations of dynamical systems on simple time scales]. {\em Lobachevskii J. Math., } 2023, Vol. 44, 1215-1222
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  12. Petrov A. A., Pilyugin S. Yu. [Shadowing near nonhyperbolic fixed points]. Discrete Contin. Dyn. Syst. , 2014, Vol. 34, 3761-3772

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