Feldman–Katok metric is the weakest metric in some sense that makes entropy formulae valid, which can also be considered as the topological counterpart of the edit distance. In this paper, we study Feldman–Katok metric of random dynamical systems and establish topological entropy formula as well as Brin–Katok local entropy formula and Katok entropy formula on Feldman–Katok metric.
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Xie et al. (2024) studied this question.
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