On absolute nonshadowability of transitive maps

2016/06/24 by Sergey Tikhomirov, Tikhomirov, Sergey
Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.DS

paper · pdf · doi:10.48550/arxiv.1606.07716

arxiv created 2016/06/24 · arxiv updated 2016/06/27

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.

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