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arXiv · 2202.07051

Random Expansive Measures

Rafael A. Bilbao·Marlon Oliveira·Eduardo Santana
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Abstract

The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying significant type of behavior, such as chaotic one. This study aims to extend these notions into a random context and prove a relationship between relative positive entropy and random expansive measures and apply it to show that if a random dynamical system has positive relative topological entropy then the $w$-stable classes have zero measure for the conditional measures. We also prove that there exists a probability measure that is both invariant and expansive. Moreover, we obtain a relation between the notions of random expansive measures and random countably-expansive systems.

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Rafael A. Bilbao, Marlon Oliveira, Eduardo Santana. 2022-02-14. Random Expansive Measures. https://doi.org/10.1088/1361-6544/ad673f

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