R. L. Devaney. Dynamics of entire maps. in Proc. International Conference on Dynamics, Stefan Banach Center, Warsaw (to appear).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....definition. iii) Q m j 1 (z j ) 0 for 1 # j # k 1. This follows from (11) since Q 1 (z) P (z) for z # D(r) Thus Q 1 has all the required properties, except that it is not holomorphic in the annulus A(r, 2r) To make it holomorphic we use a method of M. Shishikura [17] see also [5, 8 9] for an account of Shishikura s method. The image of the annulus A(r, 2r) is contained in the invariant domain U , which is disjoint from A(r, 2r) This permits us to define a new conformal structure # in C such that it coincides with the standard conformal structure # 0 in U , and Q 1 : C, #) ....

R. L. Devaney, Dynamics of entire maps, in: Dynamical Systems and Ergodic Theory, Banach Center Publ., vol. 23, Polish Scientific Publishers, Warsaw, 1989, pp. 221-228.

.... 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. Dynamics of entire maps. in Proc. International Conference on Dynamics, Stefan Banach Center, Warsaw (to appear).

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R. L. Devaney. Dynamics of entire maps. in Proc. International Conference on Dynamics, Stefan Banach Center, Warsaw (to appear).

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