Regularity of dynamical Green’s functions
Regularity of dynamical Green’s functions
复制标题
动态格林函数的正则性
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
V. Guedj
中科院分区：
文献类型：
--
作者：
J. Diller;V. Guedj
对于复流形的亚纯映射，遍历理论和多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电流，这些电流相交以产生最大熵的度量。“足够好”通常是格林函数的正则性的一个条件。在这篇论文中，我们研究了动态格林函数的各种正则性。我们简化和推广了一些已知的结果，并证明了一些新的结果。我们还给出了一些例子，表明仅仅依靠动态格林函数的规律性在复杂动力学中所能达到的极限。
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 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.