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Wandering domains
arising from Lavaurs maps with siegel disks
Matthieu Astorg, Luka Boc Thaler and Han Peters |
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Vol. 16 (2023), No. 1, 35–88
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Abstract |
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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. |
Keywords
Fatou set, holomorphic dynamics, parabolic implosion,
polynomial mappings, skew-products, wandering Fatou
components, parabolic curves, nonautonomous dynamics
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Mathematical Subject Classification 2010
Primary: 32H50, 37F10, 37G15
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Milestones
Received: 14 October 2019
Revised: 23 February 2021
Accepted: 14 June 2021
Published: 14 April 2023
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Authors |
| Matthieu Astorg | |
| Institut Denis Poisson Collegium Sciences et Techniques Université d’Orléans Orléans France |
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| Luka Boc Thaler | |
| Faculty of Education University of Ljubljana Ljubljana Slovenia |
Institute of Mathematics, Physics
and Mechanics Ljubljana Slovenia |
| Han Peters | |
| Korteweg de Vries Institute for
Mathematics University of Amsterdam Amsterdam Netherlands |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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