共查询到18条相似文献,搜索用时 46 毫秒
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阳卫锋 《纯粹数学与应用数学》2009,25(3):530-533
主要讨论多项式的牛顿变换Julia集的对称性问题.利用复动力系统理论,证明了多项式P(z)的Julia集的对称群是其牛顿变换Np(z)的Julia集的对称群的子群.获得了Julia集为一水平直线的充分必要条件. 相似文献
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两族选代的不动点和Julia集 总被引:1,自引:0,他引:1
This paper proves that, for complex polynomials, all extraneous fixed pointsfor any iteration of Halley iterative family and another relevant iterative family arerepelling. Thus no false convergent phenomenon arises on these iterations. 相似文献
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刘刚 《纯粹数学与应用数学》2012,(5):628-634
主要研究特殊多项式的牛顿映照的动力学性质.通过研究根的分布和重数,揭示了当多项式的根关于某点具有一定的旋转对称性,且对称根的重数都相同时,此类多项式的牛顿映照要么是双曲的,要么是次双曲的.另外多项式的牛顿映照的动力学性质为多项式的某些问题提供了新的思路. 相似文献
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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
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研究有理函数及整函数Julia集的拓扑结构,刻画了有理函数Julia集的复杂性,展示了整函数在Fatou集上的动力学性质对其Julia集拓扑复杂性的影响. 相似文献
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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
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考虑反铁磁链对应的金刚石型等级晶格上的Potts模型, 研究复相变点集的性质. 这些集合是一族有理映照的Julia集, 证明了它们可能是不连通的集合, 并就其拓扑结构给出了比较完备的刻画. 相似文献
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用P表示一个度为d的首一多项式,J_P表示它的Julia集.本文得到Julia集J_P和其等势线Γ_P(R)上的d~n-阶Chebyshev多项式,并举例说明二者并不总是相等. 相似文献
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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
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Bedford Tim; Fisher Albert M.; Urbanski Mariusz 《Proceedings London Mathematical Society》2002,85(2):467-492
We define the scenery flow space at a point z in the Julia setJ of a hyperbolic rational map T : C C with degree at least2, and more generally for T a conformal mixing repellor. We prove that, for hyperbolic rational maps, except for a fewexceptional cases listed below, the scenery flow is ergodic.We also prove ergodicity for almost all conformal mixing repellors;here the statement is that the scenery flow is ergodic for therepellors which are not linear nor contained in a finite unionof real-analytic curves, and furthermore that for the collectionof such maps based on a fixed open set U, the ergodic casesform a dense open subset of that collection. Scenery flow ergodicityimplies that one generates the same scenery flow by zoomingdown towards almost every z with respect to the Hausdorff measureHd, where d is the dimension of J, and that the flow has a uniquemeasure of maximal entropy. For all conformal mixing repellors, the flow is loosely Bernoulliand has topological entropy at most d. Moreover the flow atalmost every point is the same up to a rotation, and so as acorollary, one has an analogue of the Lebesgue density theoremfor the fractal set, giving a different proof of a theorem ofFalconer. 2000 Mathematical Subject Classification: 37F15, 37F35, 37D20. 相似文献
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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
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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. 相似文献
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主要研究方程f"(z)+A(z)f'(z)+B(z)f(z)=0(A(z)),B(z)为整函数)的解、解的多项式或微分多项式这些具有无穷下级的整函数的Julia集的径向分布问题. 相似文献
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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.
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Joachim Grispolakis John C. Mayer Lex G. Oversteegen 《Transactions of the American Mathematical Society》1999,351(3):1171-1201
We obtain results on the structure of the Julia set of a quadratic polynomial with an irrationally indifferent fixed point in the iterative dynamics of . In the Cremer point case, under the assumption that the Julia set is a decomposable continuum, we obtain a building block structure theorem for the corresponding Julia set : there exists a nowhere dense subcontinuum such that , is the union of the impressions of a minimally invariant Cantor set of external rays, contains the critical point, and contains both the Cremer point and its preimage. In the Siegel disk case, under the assumption that no impression of an external ray contains the boundary of the Siegel disk, we obtain a similar result. In this case contains the boundary of the Siegel disk, properly if the critical point is not in the boundary, and contains no periodic points. In both cases, the Julia set is the closure of a skeleton which is the increasing union of countably many copies of the building block joined along preimages of copies of a critical continuum containing the critical point. In addition, we prove that if is any polynomial of degree with a Siegel disk which contains no critical point on its boundary, then the Julia set is not locally connected. We also observe that all quadratic polynomials which have an irrationally indifferent fixed point and a locally connected Julia set have homeomorphic Julia sets.