dc.contributor.author |
Barański, Krzysztof |
dc.contributor.author |
Fagella Rabionet, Núria |
dc.contributor.author |
Jarque i Ribera, Xavier |
dc.contributor.author |
Karpinska, Boguslawa |
dc.date |
2014 |
dc.identifier |
https://ddd.uab.cat/record/150738 |
dc.identifier |
urn:10.1007/s00222-014-0504-5 |
dc.identifier |
urn:oai:ddd.uab.cat:150738 |
dc.identifier |
urn:gsduab:3464 |
dc.identifier |
urn:scopus_id:84893197133 |
dc.identifier |
urn:wos_id:000345332300002 |
dc.identifier |
urn:articleid:14321297v198n3p591 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 |
dc.relation |
Ministerio de Economía y Competitividad MTM-2006-05849 |
dc.relation |
Inventiones Mathematicae ; Vol. 198 Núm. 3 (2014), p. 591-636 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
Absorbing domains |
dc.subject |
Meromorphic functions |
dc.subject |
Newton maps |
dc.title |
On the connectivity of Julia sets of meromorphic functions |
dc.type |
Article |
dc.description.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. |