Modular Chaos for Random Processes

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 Poincar´e, Li-Yorke and Devaney chaos in a single model, which can be unbounded. The research demonstrates that the dynamics of Poincar´e chaos is of exceptional use to analyze discrete and continuous-time random processes. Examples, illustrating the results are provided.
Discontinuity, Nonlinearity, and Complexity


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Citation Formats
M. Akhmet, “Modular Chaos for Random Processes,” Discontinuity, Nonlinearity, and Complexity, vol. 11, no. 2, pp. 191–201, 2022, Accessed: 00, 2022. [Online]. Available: