| Abstract: |
| We consider random holomorphic dynamical systems on the Riemann sphere. We show that a generic such system satisfies some nice properties (weak mean stability) which cannot be seen in usual iteration dynamics of a single holomorphic map. We classify generic systems in terms of averaged behavior and sequencewise dynamics. We will see many new phenomena in random holomorphic dynamical systems which cannot hold for iteration dynamics of a single holomorphic map. For the preprint, see H. Sumi, Negativity of Lyapunov Exponents and Convergence of Generic Random Polynomial Dynamical Systems and Random Relaxed Newton`s Methods, https://arxiv.org/abs/1608.05230. |
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