Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy
Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy
We consider non-i.i.d. random holomorphic dynamical systems whose choice of maps depends on Markovian rules. We show that generically, such a system is mean stable or chaotic with full Julia set. If a system is mean stable, then the Lyapunov exponent is uniformly negative for every initial value and almost …