R. L. Devaney. Julia sets and bifurcation diagrams for exponential maps. Bulletin of the American Mathematical Society, 11:167--171, 1984. Home/Search Document Not in Database Summary Related Articles Check |
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Growth in Complex Exponential Dynamics - Romera, Pastor, Alvarez, Montoya (1998) (Correct)
....Iterates of the complex exponential map z e n z n = 1 ( z C ) were studied for the first time by Misiurewicz [13] from a mathematical point of view. Latter, Baker and Rippon [14] studied the iteration of the family of complex exponential maps z e n z n = 1 l and, independently, Devaney [15] studied the iteration of the family of complex exponential maps z e n z n = 1 l . In the last two cases, the two families of maps were also studied from a mathematical point of view, but the Mandelbrot like set of each one of them was also drawn. It is easy to show that the Mandelbrot like ....
.... C p , which lies outside C 1 but is tangent to C 1 at l h h = e (a similar situation occurs in the well known Mandelbrot set, where there is a period 1 domain bounded by a cardioid and there are period p disks connected to it through only one point) Devaney called such a domain a tongue [15]. 4.1. Tongues In Fig. 1 we can see many tongues in the BRD set as, for example, tongues of periods 3, 5, 7, 9 and 11 attached to the period 1 domain bounded by the cardioid. A tongue is simply connected and extends to infinity [15] The bigger one, the period 2 tongue, is a domain tangent to C ....
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R. Devaney, Julia sets and bifurcation diagrams for exponential maps, B. Am. Math. Soc. 11, 167-171 (1984).
Random Mapping Statistics - Flajolet, Odlyzko (1990) (37 citations) (Correct)
.... 0. The first step, whose rather involved proof we omit, is to show that in the region fz j jzj e 01 ffi; z 62 Dg 8 It turns out that the t [h] z) converge to t(z) for all z in fz j z = ie 0i ; jij 1g. This follows from recent results in iteration of entire functions due to Devaney [9, 8]; however, these results do not seem to provide the necessary quantitative information we need. 15 we have e h (z) small and t [h] z) bounded away from 1, so that 4(z) is analytic there. Therefore, in order to apply Theorem 1, we only need to study 4(z) for z 2 D. The main step in the ....
R. L. Devaney. Julia sets and bifurcation diagrams for exponential maps. Bulletin of the American Mathematical Society, 11:167--171, 1984.
Random Mapping Statistics - Philippe Flajolet Inria (1990) (37 citations) (Correct)
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R. L. Devaney. Julia sets and bifurcation diagrams for exponential maps. Bulletin of the American Mathematical Society, 11:167--171, 1984.
Entire functions of slow growth whose Julia set coincides.. - Bergweiler, Eremenko (2000) (Correct)
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R. L. Devaney, Julia sets and bifurcation diagrams for exponential maps, Bull. Amer. Math. Soc. (N.S.) 11 (1984), 167-171.
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