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arXiv · 1411.1188

A two-dimensional polynomial mapping with a wandering Fatou component

Matthieu Astorg·Xavier Buff·Romain Dujardin·Han Peters·Jasmin Raissy
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Abstract

We show that there exist polynomial endomorphisms of C^2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of P^2(C). We also find real examples with wandering domains in R^2. The proof is based on parabolic implosion techniques, and is based on an original idea of M. Lyubich.

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Matthieu Astorg, Xavier Buff, Romain Dujardin, Han Peters, Jasmin Raissy. 2014-12-08. A two-dimensional polynomial mapping with a wandering Fatou component. https://arxiv.org/abs/1411.1188

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