Statistical Description of Mixed Systems (Chaotic and Regular)*

We discuss a statistical theory for Hamiltonian dynamics with a mixed
phase space, where in some parts of phase space the dynamics is
chaotic while in other parts it is regular. Transport in phase
space is dominated by sticking to complicated structures and its
distribution is universal. The survival probability in the vicinity of
the initial point is a power law in time with a universal exponent. We
calculate this exponent in the framework of the Markov Tree model
proposed by Meiss and Ott in 1986. It turns out that, inspite of many
approximations, it predicts important results quantitatively. The
calculations are extended to the quantum regime where correlation
functions and observables are studied.