Functions of small growth with no unbounded Fatou components
نویسندگان
چکیده
منابع مشابه
Functions of Small Growth with No Unbounded Fatou Components
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...
متن کاملBoundaries 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...
متن کاملGrowth 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...
متن کاملNon-existence of Unbounded Fatou Components of a Meromorphic Function Zheng Jian-hua and Piyapong Niamsup
This paper is devoted to establish sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extend some results for entire functions to meromorphic function. Actually, we shall mainly discuss non-existence of unbounded wandering domains of a meromorphic function. The case for a composition of finitely many meromorphic function with at leas...
متن کاملBoundaries of Escaping Fatou Components
Let f be a transcendental entire function and U be a Fatou component of f . We show that if U is an escaping wandering domain of f , then most boundary points of U (in the sense of harmonic measure) are also escaping. In the other direction we show that if enough boundary points of U are escaping, then U is an escaping Fatou component. Some applications of these results are given; for example, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2009
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-009-0018-z