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Pàgina inicial > Articles > Articles publicats > Brushing the hairs of transcendental entire functions |
Data: | 2012 |
Resum: | Let f be a transcendental entire function of finite order in the EremenkoLyubich class B (or a finite composition of such maps), and suppose that f is hyperbolic and has a unique Fatou component. We show that the Julia set of f is a Cantor bouquet; i. e. is ambiently homeomorphic to a straight brush in the sense of Aarts and Oversteegen. In particular, we show that any two such Julia sets are ambiently homeomorphic. We also show that if f ∈ B has finite order (or is a finite composition of such maps), but is not necessarily hyperbolic with connected Fatou set, then the Julia set of f contains a Cantor bouquet. As part of our proof, we describe, for an arbitrary function f ∈ B, a natural compactification of the dynamical plane by adding a "circle of addresses" at infinity. |
Ajuts: | Ministerio de Economía y Competitividad MTM2006-05849 Ministerio de Economía y Competitividad MTM2008-01486 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-792 |
Nota: | Agraïments: The first author is supported by Polish MNiSW Grant N N201 0234 33 and Polish MNiSW SPB-M. The third author is supported by EPSRC fellowship EP/E052851/1. All three authors are supported by the EU FP6 Marie Curie Program RTN CODY. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Publicat a: | Topology and its applications, Vol. 159 Núm. 8 (2012) , p. 2102-2114, ISSN 0166-8641 |
Postprint 19 p, 385.7 KB |