Google matrix and Ulam networks of intermittency maps.
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 beta dependent on map parameters and the Google damping factor alpha . Under certain conditions the PageRank is completely delocalized so that the Google search in such a situation becomes inefficient.
Ermann
L
L
Laboratoire de Physique Théorique (IRSAMC), Université de Toulouse-UPS, F-31062 Toulouse, France.
Shepelyansky
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DL