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Fatou-Bieberbach Domains by Wold, Erlend Fornæss is a scholarly article available to read on EtoBox.

What is Fatou-Bieberbach Domains about?

We show that for any $m\in\NN\cup\{\infty\}$ there exist $m$ disjoint FB domains whose union is dense in $\CC^k$. In fact we show that any point not in the union is a boundary point for all the domains. We construct FB domains that contains arbitrary countable collections of subvarieties of $\CC^k$, and we construct FB domains that intersect elements of countable collections of affine subspaces of $\CC^k$ in connected proper subsets. Moreover, we show that any Runge FB domain is the attracting basin for a sequence of automorphisms of $\CC^k$, although not necessarily if you only allow iteration of one automorphism. We also show that an increasing sequence of Runge $\CC^k$'s is a $\CC^k$.

Author

Wold, Erlend Fornæss

Published

2004

Language

EN