| Title: | Wandering domains arising from Lavaurs maps with Siegel disks |
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| Authors: | ID Astorg, Matthieu (Author)
ID Boc Thaler, Luka (Author)
ID Peters, Han (Author) |
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| Files: |  PDF - Presentation file, download (1,55 MB)
MD5: 704856943F87393378C225F327943A8C
 URL - Source URL, visit https://msp.org/apde/2023/16-1/p02.xhtml
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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: | The 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. |
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| Keywords: | Fatou sets, holomorphic dynamics, parabolic implosion, polynomial mappings, skew-products, wandering Fatou components, parabolic curves, nonautonomous dynamics |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 35-88 |
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| Numbering: | Vol. 16, no. 1 |
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| PID: | 20.500.12556/DiRROS-18640  |
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| UDC: | 517.53 |
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| ISSN on article: | 2157-5045 |
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| DOI: | 10.2140/apde.2023.16.35 |
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| COBISS.SI-ID: | 150202115 |
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| Publication date in DiRROS: | 09.04.2024 |
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| Views: | 1487 |
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| Downloads: | 504 |
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