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

Differential Equations
and
Control Processes

On Absolute Nonshadowability of Transitive Maps

Author(s):

Sergey Tikhomirov

Saint-Petersburg State University 14th lane 29B, Vasilievsky Island,
St. Petersburg, 199178, Russia.
Max Planck Institute for Mathematics in the Science Inselstrasse 22,
04103 Leipzig, Germany.
Doctor of Science

sergey.tikhomirov@gmail.com

Abstract:

We study shadowing property for random infinite pseudotrajectories of a continuous map f of a compact metric space. For the cases of transitive maps and transitive attractors we prove a dichotomy: either f satisfies shadowing property or random pseudotrajectory is shadowable with probability 0.

Keywords

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