On the Fatou components of two permutable transcendental entire functions
نویسندگان
چکیده
منابع مشابه
Boundaries of Unbounded Fatou Components of Entire Functions
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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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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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: Journal of Mathematical Analysis and Applications
سال: 2003
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(02)00664-9