Home > Articles > Published articles > On the connectivity of Julia sets of meromorphic functions |
Date: | 2014 |
Abstract: | We prove that every transcendental meromorphic map f with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question. |
Grants: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 Ministerio de Economía y Competitividad MTM-2006-05849 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Absorbing domains ; Meromorphic functions ; Newton maps |
Published in: | Inventiones Mathematicae, Vol. 198 Núm. 3 (2014) , p. 591-636, ISSN 1432-1297 |
Postprint 34 p, 476.4 KB |