Home > Articles > Published articles > Accesses to infinity from Fatou components |
Date: | 2017 |
Abstract: | We study the boundary behaviour of a meromorphic map f: \C C on its invariant simply connected Fatou component U. To this aim, we develop the theory of accesses to boundary points of U and their relation to the dynamics of f. In particular, we establish a correspondence between invariant accesses from U to infinity or weakly repelling points of f and boundary fixed points of the associated inner function on the unit disc. We apply our results to describe the accesses to infinity from invariant Fatou components of the Newton maps. |
Grants: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 Ministerio de Economía y Competitividad MTM2011-26995-C02-02 |
Note: | Agraïments: Supported by the Polish NCN grant decision DEC-2012/06/M/ST1/00168. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Accesses to boundary points ; Fatou components ; Inner functions ; Newton maps |
Published in: | Transactions of the American Mathematical Society, Vol. 369 Núm. 3 (2017) , p. 1835-1867, ISSN 1088-6850 |
Postprint 31 p, 7.8 MB |