Self-similarity and transport in the standard map

摘要

Anomalous transport 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 to have power-like tails and the corresponding exponents are obtained and compared to the theory.