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Wandering domains arising from Lavaurs maps with Siegel disksAstorg, Matthieu ; Boc Thaler, Luka ; Peters, HanThe first example of polynomial maps with wandering domains was constructed in 2016 by the first and last authors, together with Buff, Dujardin and Raissy. In this paper, we construct a second ... example with different dynamics, using a Lavaurs map with a Siegel disk instead of an attracting fixed point. We prove a general necessary and sufficient condition for the existence of a trapping domain for nonautonomous compositions of maps converging parabolically towards a Siegel-type limit map. Constructing a skew-product satisfying this condition requires precise estimates on the convergence to the Lavaurs map, which we obtain by a new approach. We also give a self-contained construction of parabolic curves, which are integral to this new method.Source: Analysis & PDE. - ISSN 2157-5045 (Vol. 16, no. 1, 2023, str. 35-88)Type of material - article, component part ; adult, seriousPublish date - 2023Language - englishCOBISS.SI-ID - 150202115
Author
Astorg, Matthieu |
Boc Thaler, Luka |
Peters, Han
Topics
Fatoujeve množice |
holomorfna dinamika |
parabolična implozija |
polinomske preslikave |
poševni produkti |
blodeče Fatoujeve komponente |
parabolične krivulje |
neavtonomna dinamika |
Fatou sets |
holomorphic dynamics |
parabolic implosion |
polynomial mappings |
skew-products |
wandering Fatou components |
parabolic curves |
nonautonomous dynamics
Author | Astorg, Matthieu ; Boc Thaler, Luka ; Peters, Han |
Title | Wandering domains arising from Lavaurs maps with Siegel disks |
Publication date | 2023-04-14 |
COBISS.SI-ID | 150202115 |
Publication version in repository | Publisher's version |
Publication licence | Creative Commons Attribution 4.0 International |
Embargo | Immediate publication for public |
Project(s) from which the publication was funded
Title | Acronym | Project ID | Funder |
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Analiza in geometrija | P1-0291-2022 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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https://msp.org/apde/2023/16-1/p02.xhtml |
https://dirros.openscience.si/IzpisGradiva.php?id=18640 |
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Astorg, Matthieu | |
Boc Thaler, Luka | 34560 |
Peters, Han |
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