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Title:Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces
Authors:ID Arosio, Leandro (Author)
ID Fiacchi, Matteo (Author)
ID Guerini, Lorenzo (Author)
ID Karlsson, Anders (Author)
Files:.pdf PDF - Presentation file, download (653,42 KB)
MD5: B26AAC59D66B58FE8805453A8683FEB6
 
URL URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0001870823006278
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
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 Ω⊂⊂Cq, where Ω 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 D⊂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 Bq⊂Cq, namely that for holomorphic parabolic self-maps any escaping backward orbit with bounded step always converges to a point in the boundary.
Keywords:holomorphic dynamics, non-expanding maps, Gromov hyperbolicity, horofunctions, boundary fixed points
Publication status:Published
Publication version:Version of Record
Publication date:01.03.2024
Year of publishing:2024
Number of pages:39 str.
Numbering:Vol. 439, article no. 109484
PID:20.500.12556/DiRROS-21154 New window
UDC:517.5
ISSN on article:0001-8708
DOI:10.1016/j.aim.2023.109484 New window
COBISS.SI-ID:220693251 New window
Note:
Publication date in DiRROS:08.01.2025
Views:163
Downloads:93
Metadata:XML DC-XML DC-RDF
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AROSIO, Leandro, FIACCHI, Matteo, GUERINI, Lorenzo and KARLSSON, Anders, 2024, Backward dynamics of non-expanding maps in Gromov hyperbolic metric spaces. Advances in mathematics [online]. 2024. Vol. 439, no. 109484. [Accessed 10 April 2025]. DOI 10.1016/j.aim.2023.109484. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=21154
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Record is a part of a journal

Title:Advances in mathematics
Shortened title:Adv. math.
Publisher:Elsevier
ISSN:0001-8708
COBISS.SI-ID:24891904 New window

Document is financed by a project

Funder:Other - Other funder or multiple funders
Funding programme:MIUR Excellence Department Project
Project number:CUP E83C18000100006
Funder:Other - Other funder or multiple funders
Funding programme:Progetto FIRB -Bando 2012 “Futuro in ricerca”
Project number:RBFR12W1AQ002
Name:Geometria Differenziale e Teoria Geometrica delle Funzioni
Funder:EC - European Commission
Project number:101053085
Name:Holomorphic Partial Differential Relations
Acronym:HPDR
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0291
Name:Analiza in geometrija
Funder:Other - Other funder or multiple funders
Funding programme:Swiss NSF grant
Project number:200021-212864
Funder:Other - Other funder or multiple funders
Funding programme:Swedish Research Council grant
Project number:104651320
Funder:Other - Other funder or multiple funders
Funding programme:Swiss NSF grant
Project number:200020-200400

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

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