We generalize to the transcendental setting a theorem by Goldberg and Milnor saying that fixed rays landing together separate the remaining fixed points. We will prove an analogous theorem under the minimal assumptions that fixed rays exist and land. Among the corollaries, we obtain that there are no Cremer points on the boundaries of Fatou components, and that Fatou components are separated by pairs of periodic rays landing together. We also obtain that for parabolic periodic points there is at least one ray landing for each repelling petal.
A separation theorem for transcendental entire maps Proc. Lond. Math. Soc. (3) 110 (2015), no. 2, 291--324 / Benini, A; Fagella, N. - In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6115. - 2:(2015), pp. 291-324. [10.1112/plms/pdu047]
A separation theorem for transcendental entire maps Proc. Lond. Math. Soc. (3) 110 (2015), no. 2, 291--324.
Benini A;
2015-01-01
Abstract
We generalize to the transcendental setting a theorem by Goldberg and Milnor saying that fixed rays landing together separate the remaining fixed points. We will prove an analogous theorem under the minimal assumptions that fixed rays exist and land. Among the corollaries, we obtain that there are no Cremer points on the boundaries of Fatou components, and that Fatou components are separated by pairs of periodic rays landing together. We also obtain that for parabolic periodic points there is at least one ray landing for each repelling petal.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
