共查询到10条相似文献,搜索用时 0 毫秒
1.
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
2.
Let P be a polynomial with a connected Julia set J. We use continuum theory to show that it admits a finest monotone map φ onto a locally connected continuumJP∼, i.e. a monotone map φ:J→JP∼ such that for any other monotone map ψ:J→J′ there exists a monotone map h with ψ=h°φ. Then we extend φ onto the complex plane C (keeping the same notation) and show that φ monotonically semiconjugates PC| to a topological polynomialg:C→C. If P does not have Siegel or Cremer periodic points this gives an alternative proof of Kiwi's fundamental results on locally connected models of dynamics on the Julia sets, but the results hold for all polynomials with connected Julia sets. We also give a characterization and a useful sufficient condition for the map φ not to collapse all of J into a point. 相似文献
3.
Alexander M. Blokh John C. Mayer Lex G. Oversteegen 《Proceedings of the American Mathematical Society》1999,127(4):1215-1220
We consider a rational map of the Riemann sphere with normalized Lebesgue measure and show that if there is a subset of the Julia set of positive -measure whose points have limit sets not contained in the union of the limit sets of recurrent critical points, then for -a.e. point and is conservative, ergodic and exact.
4.
Alexander Blokh Lex Oversteegen 《Transactions of the American Mathematical Society》2004,356(1):119-133
We study topological dynamics on unshielded planar continua with weak expanding properties at cycles for which we prove that the absence of wandering continua implies backward stability. Then we deduce from this that a polynomial with a locally connected Julia set is backward stable outside any neighborhood of its attracting and neutral cycles. For a conformal measure this easily implies that one of the following holds: 1. for -a.e. , ; 2. for -a.e. , for a critical point depending on .
5.
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
6.
Infinitely Renormalizable Quadratic Polynomials 总被引:2,自引:0,他引:2
Yunping Jiang 《Transactions of the American Mathematical Society》2000,352(11):5077-5091
We prove that the Julia set of a quadratic polynomial which admits an infinite sequence of unbranched, simple renormalizations with complex bounds is locally connected. The method in this study is three-dimensional puzzles.
7.
Clinton P. Curry John C. Mayer E. D. Tymchatyn 《Proceedings of the American Mathematical Society》2008,136(11):4045-4055
We show that a plane continuum is indecomposable iff has a sequence of not necessarily distinct complementary domains satisfying the double-pass condition: for any sequence of open arcs, with and , there is a sequence of shadows , where each is a shadow of , such that . Such an open arc divides into disjoint subdomains and , and a shadow (of ) is one of the sets .
8.
作者分析了重根牛顿变换的Julia集理论,并利用迭代法构造了标准牛顿变换、松弛牛顿变换和重根牛顿变换的Julia集.采用实验数学方法,作者得出如下结论:(1)函数f(z)=zα(zβ-1) 的三种牛顿变换Julia集的中心为原点目具有β倍的旋转对称性; (2)三种牛顿变换Julia集的重根吸引域对α具有敏感的依赖性;(3)由于的零点是松弛牛顿变换的中性或斥性不动点,故松弛牛顿变换的Julia集中不存在单根吸引域;(4)由于∞点不是重根牛顿变换的不动点,故重根牛顿变换的Julia集中多为重根和单根吸引域;(5)重根牛顿法受计算误差影响最小,松弛牛顿法次之, 标准牛顿法最大. 相似文献
9.
Eric L. McDowell Sam B. Nadler Jr. 《Proceedings of the American Mathematical Society》1996,124(4):1271-1276
The notion of an absolute fixed point set in the setting of continuum-valued maps will be defined and characterized.
10.
Eric L. McDowell 《Proceedings of the American Mathematical Society》1998,126(12):3733-3741
The notion of a multi-valued absolute fixed point set (MAFS) will be defined and characterized in the setting of set-valued maps with images containing multiple components.