Modular chaos for random processes
Dynamical Systems
2020-04-30 v2 Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.2004.08383,
title = {Modular chaos for random processes},
author = {Marat Akhmet},
journal= {arXiv preprint arXiv:2004.08383},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1905.02198