Fatou-Bieberbach Domains
| dc.creator | Wold, Erlend Fornæss | |
| dc.date | 2004-10-07 | |
| dc.date | 2005-02-26 | |
| dc.date.accessioned | 2026-07-07T05:13:03Z | |
| dc.date.available | 2026-07-07T05:13:03Z | |
| dc.description | 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 $\CC^k$. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410212 | |
| dc.identifier | http://arxiv.org/abs/math/0410212 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72807 | |
| dc.subject | Complex Variables | |
| dc.subject | 32H023; 32H50 | |
| dc.title | Fatou-Bieberbach Domains | |
| dc.type | text |