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

Differential Equations
Control Processes

On Absolute Nonshadowability of Transitive Maps


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


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.



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