Universal exponent for transport in mixed Hamiltonian dynamics

We compute universal distributions for the transition probabilities of a Markov model for transport in the mixed phase space of area-preserving maps and verify that the survival probability distribution for trajectories near an infinite island-around-island hierarchy exhibits, on average, a power-law decay with exponent $\gamma =1.57$. This exponent agrees with that found from simulations of the Hénon and Chirikov-Taylor maps. This provides evidence that the Meiss-Ott Markov tree model describes the transport for mixed systems.