发表机构
Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM)（印度科学教育研究所特里凡得琅分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对全纯对应建立庞加莱重现与卡茨定理，引入诱导对应并证明其继承遍历性，同时刻画遍历测度、证明前向轨道稠密性及罗赫林-角谷型引理。
AI 中文摘要
全纯对应的庞加莱重现定理为研究首次返回时间以及由此在该背景下诱导出的动力系统提供了自然框架。在建立了全纯对应首次返回时间平均值的卡茨定理版本之后，我们引入了诱导对应的概念，类似于映射动力学的情形，并证明它继承了全纯对应的遍历性。此外，我们刻画了相对于所考虑的全纯对应的遍历测度，在温和条件下建立了前向轨道的稠密性，并证明了罗赫林-角谷型引理。
英文摘要
The Poincaré recurrence theorem for a holomorphic correspondence provides a natural framework for studying the first return time and a dynamical system thus induced, in this setting. After establishing a version of the Kac's theorem on the average of the first return times for a holomorphic correspondence, we introduce the concept of an induced correspondence, akin to the case of dynamics of maps and prove that it inherits the ergodicity of the holomorphic correspondence. Additionally, we characterise the ergodic measures with respect to the considered holomorphic correspondence, establish the density of forward orbits under mild conditions and prove a Rokhlin-Kakutani type lemma.
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