随机缩放系统的平衡态
Equilibrium States for Random Zooming Systems
AI总结：
本文扩展缩放系统至随机情境，证明随机缩放势平衡态的存在性与唯一性，并指出其与随机双曲势等价，涵盖最大熵测度。
摘要：
本文基于Pinheiro对确定性系统的研究，将缩放系统的概念扩展到随机情境，并利用Arbieto-Matheus-Oliveira的技术，证明了我们所称的随机缩放势（包括双曲势，可能带有临界集）的平衡态的存在性。在温和条件下，我们获得了唯一性。作为存在性的一个例子，我们给出了带有临界点的所谓随机Viana映射。我们还证明了随机缩放势类与随机双曲势类是等价的，并且都包含零势，从而给出最大熵测度。
英文摘要：
In this work, based on Pinheiro for deterministic systems, we extend the notion of zooming systems to the random context and based on the technique of Arbieto-Matheus-Oliveira we prove the existence of equilibrium states for which we call random zooming potentials, that include the hyperbolic ones, possibly with the presence of a critical set. With a mild condition, we obtain uniqueness. As an example of existence, we have the so-called random Viana maps with critical points. We also prove that the classes of random zooming potentials and random hyperbolic potentials are equivalent and also contain the null potential, giving measures of maximal entropy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
