复动力学中的良集和不变密度
Nice sets and invariant densities in complex dynamics
摘要：
在复动力学中，我们构造了一个所谓的好集（第一个返回映射是马尔可夫）周围的任何点，这是在朱利亚集，但不是在后奇异集，适应建设胡安里维拉-莱特列。这简化了对绝对连续不变测度的研究。本文证明了Kotus和Swiatek最近的一个定理的逆定理，即对一类亚纯映射，绝对连续的不变测度是有限的当且仅当满足可积性条件.
英文摘要：
In complex dynamics, we construct a so-called nice set (one for which the first return map is Markov) around any point which is in the Julia set but not in the post-singular set, adapting a construction of Juan Rivera-Letelier. This simplifies the study of absolutely continuous invariant measures. We prove a converse to a recent theorem of Kotus and Swiatek, so for a certain class of meromorphic maps the absolutely continuous invariant measure is finite if and only if an integrability condition is satisfied.
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。
