Self-similarity symmetry and fractal distributions in iterative dynamics of dissipative mappings

Abstract:
We 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: f(x)=g(x)f(kx), k<1. We discuss linear models as well as nonlinear systems with chaotic behavior including dissipative circuits with delayed feedback.

Joint work with Boris Rubinstein (University of California, Davis, USA).