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

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

2007-11-21

arxiv.org/abs/0711.3357v1

Physics

Mathematical Physics

10 pages, one figure

Scientific paper

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, relating an unknown function $f(x)$ to $f(\kappa x)$ (for example, ${f(x)=g(x)f(\kappa x)}$). We discuss simple linear models as well as nonlinear systems with chaotic behavior including dissipative circuits with delayed feedback.

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