Per citar aquest document: http://ddd.uab.cat/record/150538
Web of Science: 6 cites,
Brushing the hairs of transcendental entire functions
Baranski, Krzysztof (University of Warsaw(Poland). Institute of Mathematics)
Jarque i Ribera, Xavier (Universitat Rovira i Virgili. Departament d’Enginyeria Informàtica i Matemàtiques)
Rempe, Lasse (University of Liverpool(UK). Department of Mathematical Sciences)

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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Publicat a: Topology and its Applications, Vol. 159 Núm. 8 (2012) , p. 2102-2114, ISSN 0166-8641

DOI: 10.1016/j.topol.2012.02.004


19 p, 385.7 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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