Trees and hairs for some hyperbolic entire maps of finite order |
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Authors: | Krzysztof Barański |
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Affiliation: | (1) Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland |
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Abstract: | Let f be an entire transcendental map of finite order, such that all the singularities of f −1 are contained in a compact subset of the immediate basin B of an attracting fixed point. It is proved that there exist geometric coding trees of preimages of points from B with all branches convergent to points from . This implies that the Riemann map onto B has radial limits everywhere. Moreover, the Julia set of f consists of disjoint curves (hairs) tending to infinity, homeomorphic to a half-line, composed of points with a given symbolic itinerary and attached to the unique point accessible from B (endpoint of the hair). These facts generalize the corresponding results for exponential maps. Research supported by Polish KBN Grant No 2 P03A 034 25. |
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Keywords: | 37F10 30D40 30D05 |
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