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1.
This paper discusses the limit functions of a random iteration system formed by finitely many rational functions. Applying these results we prove that a hyperbolic iteration system has no wandering domain and that its limit functions are constant. Finally the continuity on its Julia set is considered.  相似文献   

2.
We shall construct a pinched circle model of the Julia set of a topological polynomial without recourse to the theory of analytic functions. By using this model, we study conditions under which a topological polynomial has no wandering domain.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
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  相似文献   

6.
Let f be a rational function of degree d > 1 on the projective line over a possibly non-archimedean algebraically closed field. A well-known process initiated by Brolin considers the pullbacks of points under iterates of f, and produces an important equilibrium measure. We define the asymptotic Fekete property of pullbacks of points, which means that they mirror the equilibrium measure appropriately. As application, we obtain an error estimate of equidistribution of pullbacks of points for C 1-test functions in terms of the proximity of wandering critical orbits to the initial points, and show that the order is ${O(\sqrt{kd^{-k}})}$ upto a specific exceptional set of capacity 0 of initial points, which is contained in the set of superattracting periodic points and the omega-limit set of wandering critical points from the Julia set or the presingular domains of f. As an application in arithmetic dynamics, together with a dynamical Diophantine approximation, these estimates recover Favre and Rivera-Letelier’s quantitative equidistribution in a purely local manner.  相似文献   

7.
On the dynamics of composite entire functions   总被引:3,自引:0,他引:3  
Letf andg be nonlinear entire functions. The relations between the dynamics off⊗g andg⊗f are discussed. Denote byℐ (·) andF(·) the Julia and Fatou sets. It is proved that ifzC, thenz∈ℐ8464 (f⊗g) if and only ifg(z)∈ℐ8464 (g⊗f); ifU is a component ofF(fg) andV is the component ofF(gg) that containsg(U), thenU is wandering if and only ifV is wandering; ifU is periodic, then so isV and moreover,V is of the same type according to the classification of periodic components asU. These results are used to show that certain new classes of entire functions do not have wandering domains. The second author was supported by Max-Planck-Gessellschaft ZFDW, and by Tian Yuan Foundation, NSFC.  相似文献   

8.
庄伟 《数学杂志》2007,27(2):177-180
本文研究了几何有限有理函数的复解析动力性质.利用Markov划分与共形迭代函数系统的理论,获得了几何有限有理函数Julia集的性质.如有理函数是几何有限的,且Julia集是连通的,则Julia集的Hausdorff维数为1当且仅当Julia集为一圆周或直线的一段.  相似文献   

9.
In the present work we expand our previous work in [1] by introducing the Julia Deviation Distance and the Julia Deviation Plot in order to study the stability of the Julia sets of noise-perturbed Mandelbrot maps. We observe a power-law behaviour of the Julia Deviation Distance of the Julia sets of a family of additive dynamic noise Mandelbrot maps from the Julia set of the Mandelbrot map as a function of the noise level. Additionally, using the above tools, we support the invariance of the Julia set of a noise-perturbed Mandelbrot map under different noise realizations.  相似文献   

10.
The symmetries of Julia sets of Newton’s method is investigated in this paper. It is shown that the group of symmetries of Julia set of polynomial is a subgroup of that of the corresponding standard, multiple and relax Newton’s method when a nonlinear polynomial is in normal form and the Julia set has finite group of symmetries. A necessary and sufficient condition for Julia sets of standard, multiple and relax Newton’s method to be horizontal line is obtained.  相似文献   

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