Non-Autonomous Basins of Attraction With 4-Dimensional Boundaries

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We study whether the basin of attraction of a sequence of automorphisms of $\mathbb{C}^k$ is biholomorphic to $\mathbb{C}^k$. In particular we show that given any sequence of automorphisms with the same attracting fixed point, the basin is biholomorphic to $\mathbb{C}^k$ if the maps are repeated often enough. We also construct Fatou-Bieberbach domains whose boundaries are 4-dimensional.
15 pages

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Complex Variables, 32H02, 32H50

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http://salesiana.dossiersoluciones.com/handle/123456789/72805

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0410210
 http://arxiv.org/abs/math/0410210

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arXiv