Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy
Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy
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非独立同分布
DOI：
10.1088/1361-6544/ac4a89
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发表时间：
2022
期刊：
影响因子：
1.7
通讯作者：
Hiroki Sumi and Takayuki Watanabe
中科院分区：
文献类型：
--
作者：
Nakamura Fumihiko;Nakano Yushi;Toyokawa Hisayoshi;Yano Kouji;Hiroki Sumi and Takayuki Watanabe
我们考虑非独立同分布随机全纯动力系统，其映射的选择取决于马尔可夫规则。我们证明，一般来说，这样的系统在完整的 Julia 集下是平均稳定或混沌的。如果系统是平均稳定的，则李亚普诺夫指数对于每个初始值和几乎每个随机轨道都一致为负。此外，我们考虑了随机全纯动力系统族，并证明平均稳定系统集在某些条件下具有完全测度。即使对于独立同分布随机动力系统，后者也是一个新结果。
We consider non-iid 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. Moreover, we consider families of random holomorphic dynamical systems and show that the set of mean stable systems has full measure under certain conditions. The latter is a new result even for iid random dynamical systems.