Upper-bound for the number of robust parabolic curves for a class of maps tangent to identity
| dc.creator | Innocenti, Francesco Degli | |
| dc.creator | Frosini, Chiara | |
| dc.date | 2007-02-20 | |
| dc.date.accessioned | 2026-07-07T07:47:49Z | |
| dc.date.available | 2026-07-07T07:47:49Z | |
| dc.description | The Leau-Fatou flower theorem completely describes the dynamic behavior of $1-$dimensional maps tangent to the identity. In dimension two Hakim and Abate proved that if $f$ is a holomorphic map tangent to the identity in $\mathbb{C}^2$ and $ν(f)$ is the degree of the first non vanishing jet of $f-Id$ then there exist $ν(f)-1$ robust parabolic curves (RP curves for short), namely attractive petals at the origin which survive under by blow-up. The set of the exponential of holomorphic vector fields (of order greater than or equal to two), $Φ_{\geq 2}(\mathbb{C}^2,0)$, is dense in the space of germs of maps tangent to the identity. In this paper we give an upper-bound for the number of robust parabolic curves of $f\in Φ_{\geq 2}(\mathbb{C}^2,0) .$ | |
| dc.identifier | https://arxiv.org/abs/math/0702576 | |
| dc.identifier | http://arxiv.org/abs/math/0702576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124295 | |
| dc.subject | Complex Variables | |
| dc.subject | 32H50; 37F99; 34M25 | |
| dc.title | Upper-bound for the number of robust parabolic curves for a class of maps tangent to identity | |
| dc.type | text |