اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the spherical derivative of a rational function
128
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
For a rational function f we consider the norm of the derivative with respect to the spherical metric and denote by K(f) the supremum of this norm. We give estimates of this quantity K(f) both for an individual function and for sequences of iterates.
قيم البحث
اقرأ أيضاً
We examine iteration of certain skew-products on the bidisk whose components are rational inner functions, with emphasis on simple maps of the form $Phi(z_1,z_2) = (phi(z_1,z_2), z_2)$. If $phi$ has degree $1$ in the first variable, the dynamics on e
ach horizontal fiber can be described in terms of Mobius transformations but the global dynamics on the $2$-torus exhibit some complexity, encoded in terms of certain $mathbb{T}^2$-symmetric polynomials. We describe the dynamical behavior of such mappings $Phi$ and give criteria for different configurations of fixed point curves and rotation belts in terms of zeros of a related one-variable polynomial.
In 1980s, Thurston established a combinatorial characterization for post-critically finite rational maps. This criterion was then extended by Cui, Jiang, and Sullivan to sub-hyperbolic rational maps. The goal of this paper is to present a new but sim
pler proof of this result by adapting the argument in the proof of Thurstons Theorem.
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 that along any marked point the Green function of a meromorphic family of polynomials parameterized by the punctured unit disk explodes exponentially fast near the origin with a continuous error term.
We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. In particular, we describe a class of transcendental entire functions for which an analogue of the Branner-Hubbard conjectu
re holds and show that, for such functions, if K(f) is disconnected then it has uncountably many components. We give examples to show that K(f) can be totally disconnected, and we use quasiconformal surgery to construct a function for which K(f) has a component with empty interior that is not a singleton.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
