اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدLocal Connectivity of Polynomial Julia sets at Bounded Type Siegel Boundaries
64
0
0.0
(
0
)
تأليف
Jonguk Yang
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Consider a polynomial $f$ of degree $d geq 2$ that has a Siegel disk $Delta_f$ with a rotation number of bounded type. We prove that there does not exist a hedgehog containing $Delta_f$. Moreover, if the Julia set $J_f$ of $f$ is connected, then it is locally connected at the Siegel boundary $partial Delta_f$.
قيم البحث
اقرأ أيضاً
We prove that a long iteration of rational maps is expansive near boundaries of bounded type Siegel disks. This leads us to extend Petersens local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case.
We prove fixed point results for branched covering maps $f$ of the plane. For complex polynomials $P$ with Julia set $J_P$ these imply that periodic cutpoints of some invariant subcontinua of $J_P$ are also cutpoints of $J_P$. We deduce that, under c
ertain assumptions on invariant subcontinua $Q$ of $J_P$, every Riemann ray to $Q$ landing at a periodic repelling/parabolic point $xin Q$ is isotopic to a Riemann ray to $J_P$ relative to $Q$.
We show that if $P$ is a quadratic polynomial with a fixed Cremer point and Julia set $J$, then for any monotone map $ph:Jto A$ from $J$ onto a locally connected continuum $A$, $A$ is a single point.
A. Sannami constructed an example of the differentiable Cantor set embedded in the real line whose difference set has a positive measure. In this paper, we generalize the definition of the difference sets for sets of the two dimensional Euclidean spa
ce as the sets of vectors between two sets, and estimate their measures. For the quadratic map Q_c(z)=z^2+c, we obtain that the measure of the difference set of its Julia set vanishes if |c|>3+sqrt{3}.
We give an introduction to buried points in Julia sets and a list of questions about buried points, written to encourage aficionados of topology and dynamics to work on these questions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
