  We consider a model of an intelligent surfer moving on the Ulam network
generated by a chaotic dynamics in the Chirikov standard map. This directed
network is obtained by the Ulam method with a division of the phase space in
cells of fixed size forming the nodes of a Markov chain. The goal quest for
this surfer is to determine the network path from an initial node A to a final
node B with minimal resistance given by the sum of inverse transition
probabilities. We develop an algorithm for the intelligent surfer that allows
to perform the quest in a small number of transitions which grows only
logarithmically with the network size. The optimal path search is done on a
fractal intersection set formed by nodes with small Erd\"os numbers of the
forward and inverted networks. The intelligent surfer exponentially outperforms
a naive surfer who tries to minimize its phase space distance to the target B.
We argue that such an algorithm provides new hints for motion control in
chaotic flows.
