Non-i.i.d. random holomorphic dynamical systems and the probability of tending to infinity

摘要

We consider random holomorphic dynamical systems on the Riemann sphere whose choices of maps are related to Markov chains. Our motivation is to generalize the facts which hold in i.i.d. random holomorphic dynamical systems. In particular, we focus on the function T-infinity,T-tau which represents the probability of tending to infinity. We show some sufficient conditions which make T-infinity,T-tau continuous on the whole space and we characterize the Julia sets in terms of the function T-infinity,T-tau under certain assumptions.