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arXiv · 2004.08383

Modular chaos for random processes

Marat Akhmet
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Abstract

In the present paper, an essential generalization of the symbolic dynamics is considered. We apply the notions of abstract self-similar sets and the similarity map for a chaos introduction, which orbits are expanded among infinitely many modules. The dynamics is free of dimensional, metrical and topological assumptions. It unites all the three types of Poincare, Li-Yorke and Devaney chaos in a single model, which can be unbounded. The research demonstrates that the dynamics of Poincare chaos is of exceptional use to analyze discrete and continuous-time random processes. Examples, illustrating the results are provided.

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Marat Akhmet. 2020-04-16. Modular chaos for random processes. https://arxiv.org/abs/2004.08383

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