Probabilistic shadowing in linear skew products
arXiv (Cornell University)(2020)
摘要
We investigate the probability of the event that a finite random pseudotrajectory can be effectively shadowed by an exact trajectory. The main result of the work describes a class of skew products, for which this probability tends to one as the length of a pseudotrajectory tends to infinity and the value of a maximal mistake on each step tends to zero. We also show that continuous linear skew products over a Bernoulli shift, doubling map on a circle and any Anosov linear map on a torus lie in this class. The Cramer's large deviation theorem is used in the proof.
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关键词
probabilistic shadowing
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