منابع مشابه
Ja n 20 06 BAKER DOMAINS FOR NEWTON ’ S METHOD
We show that there exists an entire function without finite asymp-totic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady.
متن کاملUnivalent Baker Domains
We classify Baker domains U for entire maps with fj U univalent into three diierent types, giving several criteria which characterize them. Some new examples of such domains are presented, including a domain with disconnected boundary in C and a domain which spirals towards innnity.
متن کاملFamilies of Baker Domains Ii
Let f be a transcendental meromorphic function and U be an invariant Baker domain of f . We use estimates for the hyperbolic metric to show that there is a relationship between the size of U and the proximity of f in U to the identity function, and illustrate this by discussing how the dynamics of transcendental entire functions of the following form vary with the parameter a: f(z) = az + bzke−...
متن کاملDeformation of Entire Functions with Baker Domains
We consider entire transcendental functions f with an invariant (or periodic) Baker domain U. First, we classify these domains into three types (hyperbolic, simply parabolic and doubly parabolic) according to the surface they induce when we quotient by the dynamics. Second, we study the space of quasiconformal deformations of an entire map with such a Baker domain by studying its Teichmüller sp...
متن کاملSingularities of meromorphic functions with Baker domains
We show that if f is a transcendental meromorphic function with a finite number of poles and f has a cycle of Baker domains of period p, then there exist C > 1 and r0 > 0 such { z : 1 C r < |z| < Cr } sing(f−p) ∅, for r r0. We also give examples to show that this result fails for transcendental meromorphic functions with infinitely many poles.
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2007
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2277