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arXiv · 0711.3357

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

Vladimir Zverev·Boris Rubinstein
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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, 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.

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Vladimir Zverev, Boris Rubinstein. 2007-11-21. Self-similarity symmetry and fractal distributions in iterative dynamics of dissipative mappings. https://arxiv.org/abs/0711.3357

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