# Google matrix, dynamical attractors, and Ulam networks.

@article{Shepelyansky2010GoogleMD, title={Google matrix, dynamical attractors, and Ulam networks.}, author={Dima L. Shepelyansky and O. V. Zhirov}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2010}, volume={81 3 Pt 2}, pages={ 036213 } }

We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite-size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model generates directed Ulam networks with approximate scale-free scaling and characteristics being in certain features similar to those of the world wide web with approximate scale-free degree distributions as well as…

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