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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.
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...