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