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http://hdl.handle.net/2445/120441
Title: | Dynamic rays of bounded-type transcendental self-maps of the punctured plane |
Author: | Fagella Rabionet, Núria Martí-Pete, David |
Keywords: | Sistemes dinàmics complexos Funcions Complex dynamical systems Functions |
Issue Date: | 1-Jun-2017 |
Publisher: | American Institute of Mathematical Sciences (AIMS) |
Abstract: | We study the escaping set of functions in the class B∗, that is, transcendental self-maps of C∗ for which the set of singular values is contained in a compact annulus of C∗ that separates zero from infinity. For functions in the class B∗, escaping points lie in their Julia set. If f is a composition of finite order transcendental self-maps of C∗ (and hence, in the class B∗), then we show that every escaping point of f can be connected to one of the essential singularities by a curve of points that escape uniformly. Moreover, for every sequence e∈{0,∞}N0, we show that the escaping set of f contains a Cantor bouquet of curves that accumulate to the set {0,∞} according to e under iteration by f. |
Note: | Reproducció del document publicat a: https://doi.org/10.3934/dcds.2017134 |
It is part of: | Discrete and Continuous Dynamical Systems, 2017, vol. 37, num. 6, p. 3123-3160 |
URI: | http://hdl.handle.net/2445/120441 |
Related resource: | https://doi.org/10.3934/dcds.2017134 |
ISSN: | 1078-0947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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670381.pdf | 10.41 MB | Adobe PDF | View/Open |
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