Dynamics of slowly growing entire functions
نویسندگان
چکیده
منابع مشابه
Relative orders and slowly changing functions oriented growth analysis of composite entire functions
In the paper we establish some new results depending on the comparative growth properties of composition of entire functions using relative $L^{ast }$-order (relative $L^{ast }$-lower order) as compared to their corresponding left and right factors where $Lequiv Lleft( rright) $ is a slowly changing function.
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Complex dynamics of iterated entire holomorphic functions is an active and exciting area of research. This manuscript collects known background in this field and describes several of the most active research areas within the dynamics of entire functions. Complex dynamics, in the sense of holomorphic iteration theory, has been a most active research area for the last three decades. A number of i...
متن کاملrelative orders and slowly changing functions oriented growth analysis of composite entire functions
in the paper we establish some new results depending on thecomparative growth properties of composition of entire functionsusing relative $l^{ast }$-order (relative $l^{ast }$-lowerorder) as compared to their corresponding left and right factorswhere $lequiv lleft( rright) $ is a slowly changing function.
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The basic results of the iteration theory of rational and entire functions used in this paper are contained in the classical papers [10,11], in the survey [5] and in [15, Appendix III]. Let / b e a rational or entire function and let/" = /o . . . o /be its «th iterate. Denote by Jf(f) the set of normality of/ that is, the maximal open set on which the family of iterates is normal in the sense o...
متن کاملSlowly growing meromorphic functions and the zeros of differences
Let f be a function transcendental and meromorphic in the plane with lim inf r→∞ T (r, f) (log r)2 = 0. Let q ∈ C with |q| > 1. It is shown that at least one of the functions F (z) = f(qz)− f(z), G(z) = F (z) f(z) has infinitely many zeros. This result is sharp. MSC 2000: 30D35.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2001
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270001947x