Título:
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Non-landing hairs in Sierpinski curve Julia sets of transcendental entire maps
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Autor/a:
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Garijo, Antoni; Jarque i Ribera, Xavier; Moreno Rocha, Mónica
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Abstract:
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Agraïments: The first and second author are both partially supported by the European network 035651-2-CODY. The third author is supported by CONACyT grant 59183, CB-2006-01. |
Abstract:
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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. |
Materia(s):
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-Transcendental entire maps -Julia set -Non-landing hairs -Indecomposable continua |
Derechos:
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open access
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https://rightsstatements.org/vocab/InC/1.0/ |
Tipo de documento:
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Article |
Editor:
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Uri:
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https://ddd.uab.cat/record/150407
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