有理映照Fatou分支的连通数

Baker曾用拟共形手术的方法证明了具有任意连通数的Fatou分支的存在性,Shishikua曾建议对此给出明确的有理映照的例子,本文在Beardon工作的基础上,给出了比较完善的结果。     

The Fatou and Julia Sets of Multivalued Analytic Functions

We propose a generalization of some problems of complex dynamics which includes the study of iterations of multivalued functions and compositions of various single-valued functions. We generalize two classical results concerning the Julia set.     

拟有理映照的Fatou集

定义了拟有理映照的Fatou集,将有理映照的部分结果推广到拟有理映照,并提出了供进一步研究的问题．     

On Fatou sets concerning Yang-Lee theory

The sets of the points corresponding to the complex phases of the Potts model on the diamond hierarchcal lattice are studied. These sets are the Fatou sets of a family of rational mappings. The topological structures of these sets are described completely.     

超越整函数Fatou分支的某些性质

讨论了有限个超越整函数fi(i=1,2,…,m}迭代生成的函数g=f1 o f2 o…o fm 的Fatou分支的性质,给出了g(z)的Fatou分支有界的一个充分条件.并证明了在该条件下,对g的任意游荡域U,都有{gn}的一个子列在U上趋于∞.     

On the connectivity of the Julia set of a finitely generated rational semigroup

In this paper we show that the Julia set of a finitely generated rational semigroup is connected if the union of the Julia sets of generators is contained in a subcontinuum of . Under a nonseparating condition, we prove that the Julia set of a finitely generated polynomial semigroup is connected if its postcritical set is bounded.

     

Julia sets of permutable Holomorphic maps Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide.     

Julia sets of permutable Holomorphic maps

Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

缺项幂级数表示的超越整函数Fatou分支有界性

讨论了几类用缺项幂级数表示的超越整函数Fatou集分支的有界性,并给出了其Fatou分支均有界的充分条件.     

有限个有理函数的随机复动力系统的Julia集

本文讨论有限个有理函数生成的随机复动力系统，得到Julia集有内点的充分条件和必要条件．证明了对任意的正数，可以构造有限个多项式，彼此的Julia集之间的距离大干L，但J(f1，…，fm)含有内点但不是全平面。     

Stability of Julia sets for a quadratic random dynamical system

For a sequence (cⁿ) of complex numbers, the quadratic polynomials f_cn:= z² + C_n and the sequence (F_n) of iterates F_n: = f_cn ο ⋯ ο f_c1 are considered. The Fatou set F(C_n) is defined as the set of all such that (Fⁿ) is normal in some neighbourhood of z, while the complement J(C_n) of F(c_n) (in ) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(C_n) in the case where (c_n) is bounded. A problem put forward by Brück is solved.     

On the Fatou components of two permutable transcendental entire functions

Let f and g be two distinct permutable transcendental entire functions. Suppose further that q(g)=aq(f)+b for some nonconstant polynomial q(z) and constants a(≠0), . In this article, we will investigate the dynamical properties of f and g and show that they have the same Fatou sets with the same components.     

Dynamics of Commuting Rational Maps on Berkovich Projective Space over C_p

We study the dynamics of commuting rational maps with coefficients in Cp. By lifting the dynamics from P1(Cp) to Berkovich projective space P1 Berk, we prove that two nonlinear commuting maps have the same Berkovich Julia set and the same canonical measure. As a consequence, two nonlinear commuting maps with coefficient in Cp have the same classical Julia set. We also prove that they have the same pre-periodic Berkovich Fatou components.     

On multiply-connected Fatou components in iteration of meromorphic functions

Let be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,

     

Dynamics of commuting rational maps on Berkovich projective space over ℂ p

We study the dynamics of commuting rational maps with coefficients in Cp. By lifting the dynamics from P1（Cp） to Berkovich projective space P1 Berk, we prove that two nonlinear commuting maps have the same Berkovich Julia set and the same canonical measure. As a consequence, two nonlinear commuting maps with coefficient in Cp have the same classical Julia set. We also prove that they have the same pre-periodic Berkovich Fatou components.     

On Vertex Connectivity and Absolute Algebraic Connectivity for Graphs

Let G be a graph on n vertices with vertex connectivity v with 1 h v h n m 2. We produce an attainable upper bound on the absolute algebraic connectivity of G in terms of n and v .     

On Vertex Connectivity and Absolute Algebraic Connectivity for Graphs

Let G be a graph on n vertices with vertex connectivity v with 1 ≤ v ≤ n -2. We produce an attainable upper bound on the absolute algebraic connectivity of G in terms of n and v .     

Dynamics, topology and bifurcations of McMullen maps

We give a survey of many diff erent topological structure arise in the dynamical and parameter planes of McMullen maps.