On Newton's Method for Entire Functions
| dc.creator | Rueckert, Johannes | |
| dc.creator | Schleicher, Dierk | |
| dc.date | 2005-05-30 | |
| dc.date | 2006-05-17 | |
| dc.date.accessioned | 2026-07-07T08:24:30Z | |
| dc.date.available | 2026-07-07T08:24:30Z | |
| dc.description | The Newton map N_f of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of N_f. We study the behavior of N_f in a component V of C\U. If V can be surrounded by an invariant curve within U and satisfies the condition that each point in the extended plane has at most finitely many preimages in V, we show that V contains another immediate basin of N_f or a virtual immediate basin. A virtual immediate basin is an unbounded invariant Fatou component in which the dynamics converges to infty through an absorbing set. | |
| dc.description | 19 pages, 4 figures. Changes in Version 2: Sharpened the result in Section 4 | |
| dc.identifier | https://arxiv.org/abs/math/0505652 | |
| dc.identifier | http://arxiv.org/abs/math/0505652 | |
| dc.identifier | J London Math Soc (2) 75 (2007) 659-676 | |
| dc.identifier | doi:10.1112/jlms/jdm046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136359 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 30D05, 37F10, 37F20, 49M15 | |
| dc.title | On Newton's Method for Entire Functions | |
| dc.type | text |