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Wandering domains arising from Lavaurs maps with Siegel disksMatthieu Astorg,
Luka Boc Thaler,
Han Peters, 2023, original scientific article
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.
Keywords: Fatou sets, holomorphic dynamics, parabolic implosion, polynomial mappings, skew-products, wandering Fatou components, parabolic curves, nonautonomous dynamics
Published in DiRROS: 09.04.2024; Views: 70; Downloads: 35
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