On the Julia set of analytic self-maps of the punctured plane

نویسنده

  • Walter Bergweiler
چکیده

Let f be a non-constant and non-linear entire function, g an analytic self-map of C\{0}, and suppose that exp ◦f = g ◦ exp. It is shown that z is in the Julia set of f if and only if e is in the Julia set of g. 1991 Mathematics Subject Classification: 30D05, 58F23

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A noncommutative version of the Julia-Wolff-Carathéodory theorem

The classical Julia–Wolff–Carathéodory theorem characterizes the behaviour of the derivative of an analytic self-map of a unit disk or of a half-plane of the complex plane at certain boundary points. We prove a version of this result that applies to noncommutative self-maps of noncommutative half-planes in von Neumann algebras at points of the distinguished boundary of the domain. Our result, s...

متن کامل

Julia Sets on Rp and Dianalytic Dynamics

We study analytic maps of the sphere that project to well-defined maps on the nonorientable real surface RP. We parametrize all maps with two critical points on the Riemann sphere C∞, and study the moduli space associated to these maps. These maps are also called quasi-real maps and are characterized by being conformally conjugate to a complex conjugate version of themselves. We study dynamics ...

متن کامل

A special subspace of weighted spaces of holomorphic functions on the upper half plane

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

متن کامل

Indecomposable Continua and Misiurewicz Points in Exponential Dynamics

In this paper we describe several new types of invariant sets that appear in the Julia sets of the complex exponential functions Eλ(z) = λe z where λ ∈ C. These invariant sets consist of points that share the same itinerary under iteration of Eλ. Since these exponential functions are 2πi periodic, there are several “natural” ways (described below) to decompose the plane into countably many stri...

متن کامل

Self-similarity of Siegel disks and Hausdorff dimension of Julia sets

Let f(z) = ez + z, where θ is an irrational number of bounded type. According to Siegel, f is linearizable on a disk containing the origin. In this paper we show: • the Hausdorff dimension of the Julia set J(f) is strictly less than two; and • if θ is a quadratic irrational (such as the golden mean), then the Siegel disk for f is self-similar about the critical point. In the latter case, we als...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011