论文标题
何时有两个理性功能在局部生物形态朱莉娅集合？
When do two rational functions have locally biholomorphic Julia sets?
论文作者
论文摘要
在本文中，我们解决了以下问题，最近在算术动力学中引起的问题恢复了兴趣：在哪些条件下存在两个给定的一维理性地图的朱莉娅集合之间的局部生物形态学？特别是我们发现标准确保了这种局部同构由代数对应诱导。由于面包师，Beardon，Eremenko，Levin，Przytycki等，这扩展并统一了经典结果。证明涉及整个曲线和正电流。
In this article we address the following question, whose interest was recently renewed by problems arising in arithmetic dynamics: under which conditions does there exist a local biholomorphism between the Julia sets of two given one-dimensional rational maps? In particular we find criteria ensuring that such a local isomorphism is induced by an algebraic correspondence. This extends and unifies classical results due to Baker, Beardon, Eremenko, Levin, Przytycki and others. The proof involves entire curves and positive currents.
