Google matrix and Ulam networks of intermittency maps

Details Google matrix and Ulam networks of intermittency maps Google matrix and Ulam networks of intermittency maps

2009-11-19

arxiv.org/abs/0911.3823v1

PhysRev E. 81, 03622 (2010)

Computer Science

Information Retrieval

7 pages, 14 figures, research done at Quantware http://www.quantware.ups-tlse.fr/

Scientific paper

10.1103/PhysRevE.81.036221

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.

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