Fatou components of entire functions of small growth
نویسندگان
چکیده
منابع مشابه
Growth Conditions for Entire Functions with Only Bounded Fatou Components
Let f be a transcendental entire function of order < 1/2. We denote the maximum and minimum modulus of f by M(r, f) = max{|f(z)| : |z| = r} and m(r, f) = min{|f(z)| : |z| = r}. We obtain a minimum modulus condition satisfied by many f of order zero that implies all Fatou components are bounded. A special case of our result is that if log logM(r, f) = O(log r/(log log r)) for some K > 1, then th...
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An unbounded Fatou component U of a transcendental entire function is simplyconnected. The paper studies the boundary behaviour of the Riemann map Ψ of the disc D to U , in particular the set Θ of ∂D where the radial limit of Ψ is ∞ . If U is not a Baker domain and ∞ is accessible in U , then Θ is dense in ∂D . If U is a Baker domain in which f is not univalent, Θ contains a non-empty perfect s...
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We prove a form of the cosπρ theorem which gives strong estimates for the minimum modulus of a transcendental entire function of order zero. We also prove a generalisation of a result of Hinkkanen that gives a sufficient condition for a transcendental entire function to have no unbounded Fatou components. These two results enable us to show that there is a large class of entire functions of ord...
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متن کاملIn memory of Noel Baker ENTIRE FUNCTIONS WITH BOUNDED FATOU COMPONENTS
Starting with the work of I.N. Baker that appeared in 1981, many authors have studied the question of under what circumstances every component of the Fatou set of a transcendental entire function must be bounded. In particular, such functions have no domains now known as Baker domains, and no completely invariant domains. There may be wandering domains but not the familiar and more easily const...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1999
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385799146753