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1.
By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering
lemma recently proved by Kahn and Lyubich, we prove that a component of the filled-in Julia set of any polynomial is a point
if and only if its forward orbit contains no periodic critical components. It follows immediately that the Julia set of a
polynomial is a Cantor set if and only if each critical component of the filled-in Julia set is aperiodic. This result was
a conjecture raised by Branner and Hubbard in 1992.
This work was supported by the National Natural Science Foundation of China 相似文献
2.
The topology of Julia sets for polynomials 总被引:1,自引:0,他引:1
尹永成 《中国科学A辑(英文版)》2002,45(8):1020-1024
We prove that wandering components of the Julia set of a polynomial are singletons provided each critical point in a wandering
Julia component is non-recurrent. This means a conjecture of Branner-Hubbard is true for this kind of polynomials 相似文献
3.
讨论了更广泛的拟多项式映射,研究了拟多项式的迭代,证明了关于逃逸集,充满 Julia集和Julia集的几个定理.推广了多项式动力系统的相关结果. 相似文献
4.
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
5.
In this note,it is shown that if a rational function fofdegree≥2 has a nonempty set of buried points ,then for a generic choice of the point z in the Julia set ,z is a buried point ,and if the Julia set is disconnected,it has uncountably many buried components. 相似文献
6.
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.
7.
Yin Yongcheng 《数学年刊B辑(英文版)》1998,19(1):77-80
THETOPOLOGYOFJULIASETSFORGEOMETRICALLYFINITEPOLYNOMIALSYINYONGCHENGManuscriptreceivedJune3,1995.RevisedApril3,1997.Instit... 相似文献
8.
9.
DynamicsofPolynomialAutomorphismsofC~N¥ZhangWenjun(HenanUniversity,Kaifeng,P.R.Chian,475001)Abstract:Thispaperisassignedtodis?.. 相似文献
10.
Ioannis Andreadis 《Applied mathematics and computation》2010,217(6):2883-2890
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
11.
本文用单叶函数中的面积定理及Garabedian-Schiffer不等式的有关推论.给出了求多项式的填充Julia集及Mandelbrot集面积的方法及直径的上界估计,从而给A.Douady所提的有关问题一个回答. 相似文献
12.
孙道椿 《数学物理学报(A辑)》2006,26(2):161-167
该文运用Hausdorff意义下的极限研究了有理动力系统的Julia集, 用新的思路证明了几个关于Julia集的定理. 为计算机作Julia集提供了更多的理论根据. 相似文献
13.
对于d≥2,考虑多项式族Pc=Zd+c,c∈C.Kc={z∈C|{Pcn(z)}n≥0有界}为Pc的填充Julia集,Jc=(?)Kc为其Julia集.HD(Jc)为Jc的Hausdorff维数.设ω(0)为Pc0的临界点0的轨道的聚点集.我们假定Pc0在ω(0)上是扩张的,且O∈Jc0,|c0|>ε>0.如果一序列Cn→c0,则Jcn→Jc0,Kcn→Jc0,在Hausdorff拓扑下.如果存在一常数C1>0和一序列cn→c0,使得d(cn,Jc0)≥C1|cn-c0|1+1/d,则HD(Jcn)→HD(Jc0).这里d(cn,Jc0)为cn与Jc0间距离. 相似文献
14.
15.
Cunji Yang 《分析论及其应用》2009,25(4):317-324
Based on the work of McMullen about the continuity of Julia set for rational functions, in this paper, we discuss the continuity
of Julia set and its Hausdorff dimension for a family of entire functions which satisfy some conditions. 相似文献
16.
We study the family of renormalization transformations of the generalized d -dimensional diamond hierarchical Potts model in statistical mechanic and prove that their Julia sets and non-escaping loci are always connected, where d?2. In particular, we prove that their Julia sets can never be a Sierpiński carpet if the parameter is real. We show that the Julia set is a quasicircle if and only if the parameter lies in the unbounded capture domain of these models. Moreover, the asymptotic formula of the Hausdorff dimension of the Julia set is calculated as the parameter tends to infinity. 相似文献
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18.
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. 相似文献
19.
Weifeng Yang 《Applied mathematics and computation》2010,217(6):2490-2494
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
20.
We prove that the only possible biaccessible points in the Julia set of a Cremer quadratic polynomial are the Cremer fixed point and its preimages. This gives a partial answer to a question posed by C. McMullen on whether such a Julia set can contain any biaccessible point at all.