Modular Chaos for Random Processes

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2022-1-01

Author

Akhmet, Marat

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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.

Subject Keywords

Domain structured chaos, Modular chaos, Discrete stochastic processes, Continuous random processes, Chaotic random processes, Symbolic dynamics

URI

https://hdl.handle.net/11511/97713

Journal

Discontinuity, Nonlinearity, and Complexity

DOI

https://doi.org/10.5890/dnc.2022.06.001

Collections

Department of Mathematics, Article

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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: https://hdl.handle.net/11511/97713.