Google matrix and Ulam networks of intermittency maps
| Title: | Google matrix and Ulam networks of intermittency maps |
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| Authors: | Ermann, Leonardo, Shepelyansky, Dima D. L. |
| Source: | PhysRev E. 81, 03622 (2010) |
| Publication Year: | 2009 |
| Collection: | Computer Science Nonlinear Sciences Condensed Matter Physics (Other) |
| Subject Terms: | Computer Science - Information Retrieval, Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Nonlinear Sciences - Chaotic Dynamics, Physics - Physics and Society |
| More Details: | 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. Comment: 7 pages, 14 figures, research done at Quantware http://www.quantware.ups-tlse.fr/ |
| Document Type: | Working Paper |
| DOI: | 10.1103/PhysRevE.81.036221 |
| Access URL: | http://arxiv.org/abs/0911.3823 |
| Accession Number: | edsarx.0911.3823 |
| Database: | arXiv |
| DOI: | 10.1103/PhysRevE.81.036221 |
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