On absolute nonshadowability of transitive maps

Sergey Tikhomirov

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Submission date: 22. Jun. 2016
Pages: 12
published in: Differential equations and control processes, 2016 (2016) 3, p. 57-65 
Bibtex
MSC-Numbers: 37C50, 37Hxx
Keywords and phrases: Shadowing, transitivity, attractor, Markov chain
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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.