动力学格林函数的正则性
Regularity of Dynamical Green Functions
摘要：
对于复流形上的亚纯映射，遍历论和多位势理论是密切相关的。在足够好的情况下，动态定义的格林函数产生不变的电流，这些电流相交以产生最大熵的测量。“足够好”常常是格林函数正则性的一个条件。在本文中，我们看看各种已被认为是动态格林函数的正则性。我们简化和推广了一些已知的结果，并证明了其他几个全新的结果。我们还给出了一些例子，表明人们可以希望实现的限制，在复杂的动力学仅仅依靠一个动态格林函数的规律性。
英文摘要：
For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green's functions give rise to invariant currents which intersect to yield measures of maximal entropy. `Nice enough' is often a condition on the regularity of the Green's function. In this paper we look at a variety of regularity properties that have been considered for dynamical Green's functions. We simplify and extend some known results and prove several others which are entirely new. We also give some examples indicating the limits of what one can hope to achieve in complex dynamics by relying solely on the regularity of a dynamical Green's function.
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。
