北海道力学系webセミナー: The generic dichotomy for non-i.i.d. random holomorphic dynamical systems(渡邉 天鵬 （京都大学）)

Time：2020年6月16日(火)　15:00～16:00

Speaker：渡邉 天鵬（京都大学）

Title：The generic dichotomy for non-i.i.d. random holomorphic dynamical system

Abstract：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 every random orbit. This generalizes a result for i.i.d. random dynamical systems of rational maps. We also consider the bifurcations of families of Markov random dynamical systems. We show that the mean stability locus is thick from the measure-theoretic viewpoint. This is a new result even for i.i.d. random systems.

世話役: 豊川（北大理）, 行木（北大理）, 中村（北見工大）

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