共查询到18条相似文献,搜索用时 265 毫秒
1.
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
2.
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
3.
尹永成 《数学年刊A辑(中文版)》1999,(5)
本文证明了半双曲有理映射Julia集的局部连通性,推广了Carleson-Jones-Yoccoz关于多项式的结果,同时还考虑了半双曲有理映射Julia集的面积问题. 相似文献
4.
偶四次多项式Julia集的连通性 总被引:1,自引:0,他引:1
本文推广了Branner-Hubbard-Yoccoz拼图技巧来研究偶四次多项式填充Julia集的连通性,得到类似Branner-Hubbard关于三次多项式的定理. 相似文献
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本文推广了Branner-Hubbard-Yoccoz拼图技巧来研究偶四次多项式填充Julia集的连通性,得到类似Branner-Hubbard关于三次多项式的定理。 相似文献
6.
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
7.
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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对有理函数证明了:如果Julia集不连通,Fatou集没有完全不变分支,则Julia集存在淹没分支;对有限型超越整函数证明了:如果Fatou集不连通,则Julia集上存在淹没点集的无界连续统. 相似文献
11.
Yu Zhai 《数学学报(英文版)》2010,26(11):2199-2208
In 1992, Branner and Hubbard raised a conjecture that the Julia set of a polynomial is a Cantor set if and only if each critical component of its filled-in Julia set is not periodic. This conjecture was solved recently. In this paper, we generalize this result to a class of rational functions. 相似文献
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DynamicsofPolynomialAutomorphismsofC~N¥ZhangWenjun(HenanUniversity,Kaifeng,P.R.Chian,475001)Abstract:Thispaperisassignedtodis?.. 相似文献
13.
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
14.
乔建永 《中国科学A辑(英文版)》2003,46(3):415-431
The sets of the points corresponding to the phase transitions of the Potts model on the diamond hierarchical lattice for antiferromagnetic coupling are studied. These sets are the Julia sets of a family of rational mappings. It is shown that they may be disconnected sets. Furthermore, the topological structures of these sets are described completely. 相似文献
15.
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
16.
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
17.
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.
18.
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