Anomalous transpor is investigated for the Standard Map. A chain of exact self similar islands in the vicinity of the period 5 accelerator island is found for a particular value of the map parameter. The transport is found to be superdiffusive with an anomalous exponent related to the characteristic temporal and spatial scaling parameters of the island chain. The value of the transport exponent is compared to the theory. The escape time distribution and Poincare recurrence distribution are found t o have power-like tails and the corresponding exponents are obtained and compared t o the theory.

Anomalous transport is investigated near threshold in the standard map. Very long time flights, and a large anomaly in the transport, are shown to be associated with a new form of multi-island structures causing orbit sticking. The phase space structure of these traps, and the exponents of the characteristic long time tails associated with them are determined. In general these structures are very complex, but some cases, consisting of layers of islands, allow simple modeling. (c) 1998 American Institute of Physics.

We introduce a method to infer lead-lag networks of agents' actions in complex systems. These networks open the way to both microscopic and macroscopic states prediction in such systems. We apply this method to trader-resolved data in the foreign exchange market. We show that these networks are remarkably persistent, which explains why and how order flow prediction is possible from trader-resolved data. In addition, if traders' actions depend on past prices, the evolution of the average price paid by traders may also be predictable. Using random forests, we verify that the predictability of both the sign of order flow and the direction of average transaction price is strong for retail investors at an hourly time scale, which is of great relevance to brokers and order matching engines. Finally, we argue that the existence of trader lead-lag networks explains in a self-referential way why a given trader becomes active, which is in line with the fact that most trading activity has an endogenous origin.