通过赫格洛茨表示法确定有限位移的特征

arXiv - MATH - Complex Variables Pub Date : 2024-07-15 DOI:arxiv-2407.10664

Francisco J. Cruz-Zamorano

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引用次数: 0

摘要

本文给出了有限位移抛物线自映射的赫尔格洛茨表示的完整特征。这改进了康特雷拉斯、德西亚兹-马德里加尔和庞梅伦克之前的结果。我们还推导出了这些函数向其登喜路-沃尔夫点收敛的速率，从而改进了库鲁、西奥多西阿迪斯和扎尔瓦里斯在连续环境下的相关结果。

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Characterization of finite shift via Herglotz's representation

A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, D\'iaz-Madrigal, and Pommerenke. We also derive some consequences for the rate of convergence of these functions to their Denjoy-Wolff point, improving a related result of Kourou, Theodosiadis, and Zarvalis for the continuous setting.

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arXiv - MATH - Complex Variables

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