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Dynamic rays of bounded-type transcendental self-maps of the punctured plane
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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.
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FAGELLA RABIONET, Núria and MARTÍ-PETE, David. Dynamic rays of bounded-type transcendental self-maps of the punctured plane. Discrete and Continuous Dynamical Systems. 2017. Vol. 37, num. 6, pags. 3123-3160. ISSN 1078-0947. [consulted: 17 of August of 2026]. Available at: https://hdl.handle.net/2445/120441