随机布拉施克乘积的同步与混沌之间的转变
The transition between synchronization and chaos for random Blaschke products
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中文总结 AI 辅助
研究随机布拉施克乘积同步与混沌转变，建立充分条件及唯一随机不动点吸引子的充要条件，以双映射余圈为例确定随机物理测度并研究临界值。
中文摘要 AI 辅助
在本文中，我们建立了一类随机圆周映射，即所谓的随机布拉施克乘积，展现同步或混沌动力学的充分条件。我们还建立了此类系统在单位圆盘中具有唯一随机不动点吸引子的充要条件。例如，对于一类双映射余圈，我们确定了随着参数变化的随机物理测度，并研究了动力学从有序到混沌转变的临界值。
英文摘要
In this paper, we establish sufficient conditions for which a class of random circle maps, the so-called random Blaschke products, exhibits either synchronization or chaotic dynamics. We also establish necessary and sufficient conditions for such systems to have a unique random fixed point attractor in the unit disc. As an example, for a class of two map cocycles, we identify the random physical measures as a parameter is varied and investigate the critical value where the dynamics transitions from order to chaos.
