2020/04/16 by Akhmet, Marat
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.2004.08383
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.