Assume that f is a transcendental entire function.The ray arg z=θ∈[0,2π]is said to be a limiting direction of the Julia set J(f)of f if there exists an unbounded sequence{z_(n)}■J(f)such that lim rn→∞ arg z_(n)=...Assume that f is a transcendental entire function.The ray arg z=θ∈[0,2π]is said to be a limiting direction of the Julia set J(f)of f if there exists an unbounded sequence{z_(n)}■J(f)such that lim rn→∞ arg z_(n)=θ.In this paper,we mainly investigate the dynamical properties of Julia sets of entire solutions of the complex differential equations F(z)f^(n)(z)+P(z,f)=0,and f^(n)+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.展开更多
基金Supported by the National Natural Science Foundation of China(11971344)。
文摘Assume that f is a transcendental entire function.The ray arg z=θ∈[0,2π]is said to be a limiting direction of the Julia set J(f)of f if there exists an unbounded sequence{z_(n)}■J(f)such that lim rn→∞ arg z_(n)=θ.In this paper,we mainly investigate the dynamical properties of Julia sets of entire solutions of the complex differential equations F(z)f^(n)(z)+P(z,f)=0,and f^(n)+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.
