Eigenvaluations
| dc.creator | Favre, Charles | |
| dc.creator | Jonsson, Mattias | |
| dc.date | 2004-10-19 | |
| dc.date | 2007-01-29 | |
| dc.date.accessioned | 2026-07-07T07:43:16Z | |
| dc.date.available | 2026-07-07T07:43:16Z | |
| dc.description | We study the dynamics in C^2 of superattracting fixed point germs and of polynomial maps near infinity. In both cases we show that the asymptotic attraction rate is a quadratic integer, and construct a plurisubharmonic function with the adequate invariance property. This is done by finding an infinitely near point at which the map becomes rigid: the critical set is contained in a totally invariant set with normal crossings. We locate this infinitely near point through the induced action of the dynamics on a space of valuations. This space carries an real-tree structure and conveniently encodes local data: an infinitely near point corresponds to a open subset of the tree. The action respects the tree structure and admits a fixed point--or eigenvaluation--which is attracting in a certain sense. A suitable basin of attraction corresponds to the desired infinitely near point. | |
| dc.description | 48 pages, 2 figures, To appear in Annales de l'ENS | |
| dc.identifier | https://arxiv.org/abs/math/0410417 | |
| dc.identifier | http://arxiv.org/abs/math/0410417 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122761 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32H50; 14R10, 13A18 | |
| dc.title | Eigenvaluations | |
| dc.type | text |