Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in \(\mathbb C^n\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1359.32016
author: Tran Vu Khanh
author: Ninh van Thu
published in: Proceedings of the American Mathematical Society
publication date: 2016-10-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1507.04501
Mathematics Subject Classification ID: 32H50
Mathematics Subject Classification ID: 37F99
zbMATH DE Number: 6640942
zbMATH Keywords: Wolff-Denjoy theorem
zbMATH Keywords: pseudoconvex domain of finite type
zbMATH Keywords: Kobayashi distance
zbMATH Keywords: \(f\)-property
MaRDI profile type: Publication
OpenAlex ID: W2964148603
arXiv ID: 1507.04501
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DOI: 10.1090/PROC/13138
title: Iterates of holomorphic self-maps on pseudoconvex domains of finite and infinite type in \(\mathbb C^n\)
review text: The famous Wolff-Denjoy theorem [\textit{J. Wolff}, C. R. Acad. Sci., Paris 182, 200--201 (1926; JFM 52.0309.03); \textit{A. Denjoy}, C. R. Acad. Sci., Paris 182, 255--257 (1926; JFM 52.0309.04)] states that if a holomorphic self-map of the unit disk has no fixed points, then its iterations converge to a constant map of the disk to a point on its boundary. The result was extended to various classes of pseudoconvex domains in \({\mathbb C}^n \) such as strongly pseudoconvex domains and pseudoconvex domains of strictly finite type in the sense of Range. The authors prove a Wolff-Denjoy-type theorem for a large class of bounded pseudoconvex domains with smooth boundary in \({\mathbb C}^n \) that includes many domains of both finite and infinite type. The key property of such domains is the \(f\)-property from [the first author, J. Geom. Anal. 26, No. 1, 616--629 (2016; Zbl 1337.32024)].
description: scientific article; zbMATH DE number 6640942