On Limiting Directions of Julia Sets of Entire Solutions of Complex Differential Equations

\nAssume that f is a transcendental entire function. The ray argz=θ∈[0,2π] is said to be a limiting direction of the Julia set J(f) of f if there exists an unbounded sequence {zn}⊆J(f) such that limrn→∞argzn=θ. In this paper, we mainly investigate the dynamical properties of Julia sets of entire solutions of the complex differential equations F(z)fn(z)+P(z,f)=0, and fn+A(z)P(z,f)=h(z), where P(z,f) is a differential polynomial in f and its derivatives, F(z),A(z) and h(z) are entire functions. We demonstrate the existence of close relationships Petrenko's deviations of the coefficients and the measures of limiting directions of entire solutions of the above two equations. \n