We consider the dynamics of a transcendental meromorphic function f(z) with only finitely many poles and prove that if / has only finitely many weakly repelling fixed points, then there is no multiply-connected wander...We consider the dynamics of a transcendental meromorphic function f(z) with only finitely many poles and prove that if / has only finitely many weakly repelling fixed points, then there is no multiply-connected wandering domain in its Fatou set.展开更多
In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The prop...In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.展开更多
Let P(z) be entire and g(z)=λ e z, λ∈C-{0}. If f=P(g) has no wandering domain, then neither does h=g(P) . The normal sets of h=g(P) and f=P(g) have no Baker domain at the same time.
Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or...Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or a transcendental singularity） of f if there exists a curve Г ： [0, 1） → C such that limt→1 F（t） = ∞ and limt→1（f o Г）（t） = a. In this paper we find relations between the asymptotic values of f, 9 and f o 9, relations between critical points of f, 9 and f o 9 and also in the case when the two functions f and 9 are semi-conjugated with another entire function.展开更多
In this paper, we mainly investigate entire solutions of complex differential equations with coefficients involving exponential functions, and obtain the dynamical properties of the solutions, their derivatives and pr...In this paper, we mainly investigate entire solutions of complex differential equations with coefficients involving exponential functions, and obtain the dynamical properties of the solutions, their derivatives and primitives. With some conditions on coefficients, for the solutions, their derivatives and their primitives, we consider the common limiting directions of Julia set and the existence of Baker wandering domain.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10231040)the Doctoral Education Program Foundation of China.
文摘We consider the dynamics of a transcendental meromorphic function f(z) with only finitely many poles and prove that if / has only finitely many weakly repelling fixed points, then there is no multiply-connected wandering domain in its Fatou set.
基金supported partly by the National Natural Science Foundation of China(11926201,12171050)the National Science Foundation of Guangdong Province(2018A030313508)。
文摘In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
文摘Let P(z) be entire and g(z)=λ e z, λ∈C-{0}. If f=P(g) has no wandering domain, then neither does h=g(P) . The normal sets of h=g(P) and f=P(g) have no Baker domain at the same time.
基金This paper is a main talk on the held in Nanjing, P. R. China, July, 2004.
文摘Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or a transcendental singularity） of f if there exists a curve Г ： [0, 1） → C such that limt→1 F（t） = ∞ and limt→1（f o Г）（t） = a. In this paper we find relations between the asymptotic values of f, 9 and f o 9, relations between critical points of f, 9 and f o 9 and also in the case when the two functions f and 9 are semi-conjugated with another entire function.
基金supported by Shanghai Center for Mathematical Science China Scholarship Council(201206105015)the National Science Foundation of China(11171119,11001057,11571049)the Natural Science Foundation of Guangdong Province in China(2014A030313422)
文摘In this paper, we mainly investigate entire solutions of complex differential equations with coefficients involving exponential functions, and obtain the dynamical properties of the solutions, their derivatives and primitives. With some conditions on coefficients, for the solutions, their derivatives and their primitives, we consider the common limiting directions of Julia set and the existence of Baker wandering domain.
