| Title: | Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces |
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| Authors: | ID Arosio, Leandro (Author)
ID Fiacchi, Matteo (Author)
ID Guerini, Lorenzo (Author)
ID Karlsson, Anders (Author) |
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| Files: |  PDF - Presentation file, download (653,42 KB)
MD5: B26AAC59D66B58FE8805453A8683FEB6
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0001870823006278
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | We study the interplay between the backward dynamics of a non-expanding self-map $f$ of a proper geodesic Gromov hyperbolic metric space $X$ and the boundary regular fixed points of $f$ in the Gromov boundary. To do so, we introduce the notion of stable dilation at a boundary regular fixed point of the Gromov boundary, whose value is related to the dynamical behaviour of the fixed point. This theory applies in particular to holomorphic self-maps of bounded domains $\Omega \subset\subset \mathbb{C}^q$, where $\Omega$ is either strongly pseudoconvex, convex finite type, or pseudoconvex finite type with $q=2$, and solves several open problems from the literature. We extend results of holomorphic self-maps of the disc $\mathbb{D}\subset \mathbb{C}$ obtained by Bracci and Poggi-Corradini. In particular, with our geometric approach we are able to answer a question, open even for the unit ball $\mathbb{B}^q\subset \mathbb{C}^q$, namely that for holomorphic parabolic self-maps any escaping backward orbit with bounded step always converges to a point in the boundary. |
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| Keywords: | holomorphic dynamics, non-expanding maps, Gromov hyperbolicity, horofunctions, boundary fixed points |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.03.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 39 str. |
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| Numbering: | Vol. 439, article no. 109484 |
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| PID: | 20.500.12556/DiRROS-21154  |
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| UDC: | 517.5 |
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| ISSN on article: | 0001-8708 |
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| DOI: | 10.1016/j.aim.2023.109484 |
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| COBISS.SI-ID: | 220693251 |
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| Note: |
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| Publication date in DiRROS: | 08.01.2025 |
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| Views: | 575 |
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| Downloads: | 279 |
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