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arXiv · 0911.3823

Google matrix and Ulam networks of intermittency maps

Leonardo Ermann·Dima D. L. Shepelyansky
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Abstract

We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the exponent $β$ dependent on map parameters and the Google damping factor $α$. Under certain conditions the PageRank is completely delocalized so that the Google search in such a situation becomes inefficient.

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BibTeXRIS

Leonardo Ermann, Dima D. L. Shepelyansky. 2009-11-19. Google matrix and Ulam networks of intermittency maps. https://doi.org/10.1103/physreve.81.036221

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