Calculation of Strong Anomalous Diffusion for the Chirikov-Taylor Model

It is widely known that the paradigmatic Chirikov-Taylor model presents enhanced (anomalous) diffusion for specific intervals of its stochasticity parameter due to islands of stability, which are elliptic orbits surrounding accelerator mode fixed points. In contrast to the normal diffusion, its effect has never been analytically calculated. Here we introduce a differential form for the Perron-Frobenius evolution operator in which normal and anomalous diffusion are treated separately through phases formed by angular wavenumbers. The anomalous diffusion coefficient is then calculated analitically resulting in a Schloemilch series with an exponent $\beta=3/2$ for the divergences. Numerical simulations support our results.