Valiron's construction in higher dimension
| dc.creator | Bracci, Filippo | |
| dc.creator | Gentili, Graziano | |
| dc.creator | Poggi-Corradini, Pietro | |
| dc.date | 2007-10-10 | |
| dc.date.accessioned | 2026-07-07T08:35:27Z | |
| dc.date.available | 2026-07-07T08:35:27Z | |
| dc.description | We consider holomorphic self-maps $\v$ of the unit ball $\B^N$ in $\C^N$ ($N=1,2,3,...$). In the one-dimensional case, when $\v$ has no fixed points in $\D\defeq \B^1$ and is of hyperbolic type, there is a classical renormalization procedure due to Valiron which allows to semi-linearize the map $ϕ$, and therefore, in this case, the dynamical properties of $ϕ$ are well understood. In what follows, we generalize the classical Valiron construction to higher dimensions under some weak assumptions on $\v$ at its Denjoy-Wolff point. As a result, we construct a semi-conjugation $σ$, which maps the ball into the right half plane of $\C$, and solves the functional equation $σ\circ \v=λσ$, where $λ>1$ is the (inverse of the) boundary dilation coefficient at the Denjoy-Wolff point of $\v$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0710.2020 | |
| dc.identifier | http://arxiv.org/abs/0710.2020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139752 | |
| dc.subject | Complex Variables | |
| dc.subject | Dynamical Systems | |
| dc.subject | 32H50; 32A10; 30D05 | |
| dc.title | Valiron's construction in higher dimension | |
| dc.type | text |