2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142587We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals. In typical cases a steady state satisfies a dilatation equation, relating an unknown function $f(x)$ to $f(κx)$ (for example, ${f(x)=g(x)f(κx)}$). We discuss simple linear models as well as nonlinear systems with chaotic behavior including dissipative circuits with delayed feedback.10 pages, one figureMathematical Physics37F25 (Primary) 37D45, 70K55 (Secondary)text