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Scopus: 4 cites, Web of Science: 4 cites,
Non-landing hairs in Sierpinski curve Julia sets of transcendental entire maps
Garijo, Antoni (Universitat Rovira i Virgili. Dept. d’Enginyeria Informàtica i Matemàtiques)
Jarque, Xavier (Universitat Rovira i Virgili. Dept. d’Enginyeria Informàtica i Matemàtiques)
Moreno-Rocha, Mónica (Centro de Investigación en Matemáticas(Mexico))

Data: 2011
Resum: We consider the family of transcendental entire maps given by fa (z) = a(z − (1 − a)) exp(z + a) where a is a complex parameter. Every map has a superattracting fixed point at z = −a and an asymptotic value at z = 0. For a > 1 the Julia set of fa is known to be homeomorphic to the Sierpi´ nski universal curve [19], thus containing embedded copies of any one-dimensional plane continuum. In this paper we study subcontinua of the Julia set that can be defined in a combinatorial manner. In particular, we show the existence of non-landing hairs with prescribed combinatorics embedded in the Julia set for all parameters a ≥ 3. We also study the relation between non-landing hairs and the immediate basin of attraction of z = −a. Even as each non-landing hair accumulates onto the boundary of the immediate basin at a single point, its closure, nonetheless, becomes an indecomposable subcontinuum of the Julia set.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Transcendental entire maps ; Julia set ; Non-landing hairs ; Indecomposable continua
Publicat a: Fundamenta Mathematicae, Vol. 214 (2011) , p. 135-160, ISSN 1730-6329

DOI: 10.4064/fm214-2-3

32 p, 489.6 KB

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