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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coexistence of nonempty Fatou sets and Julia sets with interior for transcendental Hénon maps
超Hénon映射 非空Fatou集 Julia集 内部共存性
2023/11/29
A Hénon map is a map of the form H(z, w) = (f(z) + aw, z). A main focus of interest are the Fatou sets and the Julia sets. In this lecture I will show that it is possible that the Fatou set and the Ju...
LOCAL CONNECTIVITY OF JULIA SETS AND BIFURCATION LOCI:THREE THEOREMS OF J.-C. YOCCOZ
LOCAL CONNECTIVITY JULIA SETS BIFURCATION LOCI THREE THEOREMS OF J.-C. YOCCOZ
2015/8/26
This paper consists of three parts, each devoted to a result due to J.-C. Yoccoz.The proofs are all somewhat modied, but they are also deeply in!uenced byYoccoz's work.
Convex optimization in Julia
Convex programming automati cerification symbolic computation multiple dispatch
2015/8/7
This paper describes Convex.jl, a convex optimization modeling framework in Julia. Convex.jl translates problems from a user-friendly functional language into an abstract syntax tree describing the pr...
The omega-limit sets of quadratic Julia sets
omega-limit sets of quadratic Julia sets Dynamical Systems
2012/5/9
In this paper we characterize $\w$-limit sets of dendritic Julia sets for quadratic maps. We use Baldwin's symbolic representation of these spaces as a non-Hausdorff itinerary space and prove that qua...
Symmetries of Julia sets of polynomial skew products on C^2
Complex dynamics skew product Green function
2012/4/18
We consider the symmetries of Julia sets of polynomial skew products on C^2, which are birationally conjugate to rotational products. Our main results give the classification of the polynomial skew pr...
Julia sets of uniformly quasiregular mappings are uniformly perfect
Julia uniformly quasiregular mappings uniformly perfect
2011/1/19
It is well-known that the Julia set J(f) of a rational map f : C → C is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus,with the bound depending only on f. In th...
Non-landing hairs in Sierpinski curve Julia sets of transcendental entire maps
Sierpinski curve Julia sets of transcendental entire maps math
2010/11/22
We consider the family of transcendental entire maps given by $f_a(z)=a(z-(1-a))\exp(z+a)$ where $a$ is a complex parameter. Every map has a superattracting fixed point at $z=-a$ and an asymptotic va...
Finitely Suslinian models for planar compacta with applications to Julia sets
Continuum finitely Suslinian locally connected monotone map
2010/12/1
A compactum X C is unshielded if it coincides with the boundary of the unbounded component of C\X. Call a compactum X finitely Suslinian if every collection of pairwise disjoint subcontinua of X who...
拟亚纯映射的Nevanlinna方向和Julia方向
拟亚纯映射 覆盖曲面 Julia方向 Nevanlinna方向
2009/11/12
该文应用K拟亚纯映射在角域内的一个基本不等式，得到了平面上K拟亚纯映射的Julia方向和Nevanlinna方向的一些结果。
一个非解析复映射的广义Julia集
非解析映射 广义J集 分形 演化
2009/10/21
推广了Michelitsch和Rossler所提出的由一个简单非解析映射所构造Julia集的方法,并由推广的复映射,构造出一系列实数阶的广义Julia集(简称广义J集)．
利用复变函数理论和计算机制图相结合的实验数学的方法,对广义J集的结构和演化进行了研究,结果表明：
①广义J集的几何结构依赖于参数α、R和c;
②广义J集具有对称性和分形特征;
③小数阶广义J集出现了错动和断裂...
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$f(z)=z^\alpha(z^\beta-1)$的三种牛顿变换Julia集的中心为原点且具有$\beta$倍的旋转对称性; (2) 三种牛顿变换Julia集的重根吸引域对$\alpha$具有敏感的依赖性; (3) 由于的...
多项式Julia集的连续性
Julia集 Hausdorff距离 对数容量 J－稳定性
2007/12/10
本文利用位势理论和复动力系统中的技巧，对多项式Ｊｕｌｉａ集在参数空间的连续性作了完全的刻画．