Resonances and diffusion in periodic hamiltonian maps

Chaotic diffusion in periodic Hamiltonian maps is studied by the introduction of a sequence of Markov models of transport based on the partition of phase space into resonances. The transition probabilities are given by turnstile overlap areas. The master equation has a Bloch band spectrum. A general exact expression for the diffusion coefficient D is derived. The behavior of D is examined for the sawtooth map. We find a critical scaling law for D, extending a result of Cary and Meiss. The critical scaling emerges as a collective effect of many resonances, in contrast with the standard map.