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We study the properties of the Google matrix generated by a coarse-grainedPerron-Frobenius operator of the Chirikov typical map with dissipation. Thefinite size matrix approximant of this operator is constructed by the Ulammethod. This method applied to the simple dynamical model creates the directedUlam networks with approximate scale-free scaling and characteristics beingrather similar to those of the World Wide Web. The simple dynamical attractorsplay here the role of popular web sites with a strong concentration ofPageRank. A variation of the Google parameter $\alpha$ or other parameters ofthe dynamical map can drive the PageRank of the Google matrix to a delocalizedphase with a strange attractor where the Google search becomes inefficient.

Google matrix, dynamical attractors and Ulam networks