  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.
