On a Question of Eremenko concerning Escaping Components of Entire Functions

نویسنده

  • LASSE REMPE
چکیده

Let f be an entire function with a bounded set of singular values, and suppose furthermore that the postsingular set of f is bounded. We show that every component of the escaping set I(f) is unbounded. This provides a partial answer to a question of Eremenko.

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

On a Question of Eremenko concerning Escaping Sets of Entire Functions (draft)

Let f be an entire function of finite order whose set of singular values is bounded or, more generally, a finite composition of such functions. We show that every escaping point of f can be connected to ∞ by a curve in I(f). This provides a positive answer to a question of Eremenko for a large class of entire functions.

متن کامل

Functions of Small Growth with No Unbounded Fatou Components

We prove a form of the cosπρ theorem which gives strong estimates for the minimum modulus of a transcendental entire function of order zero. We also prove a generalisation of a result of Hinkkanen that gives a sufficient condition for a transcendental entire function to have no unbounded Fatou components. These two results enable us to show that there is a large class of entire functions of ord...

متن کامل

Rigidity of Escaping Dynamics for Transcendental Entire Functions

We prove an analog of Böttcher’s theorem for transcendental entire functions in the Eremenko-Lyubich class B. More precisely, let f and g be entire functions with bounded sets of singular values and suppose that f and g belong to the same parameter space (i.e., are quasiconformally equivalent in the sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to the set of points ...

متن کامل

Functions of Genus Zero for Which the Fast Escaping Set Has Hausdorff Dimension Two

We study a family of transcendental entire functions of genus zero, for which all of the zeros lie within a closed sector strictly smaller than a half-plane. In general these functions lie outside the Eremenko-Lyubich class. We show that for functions in this family the fast escaping set has Hausdorff dimension equal to two.

متن کامل

The Growth Rate of an Entire Function and the Hausdorff Dimension of Its Julia Set

Let f be a transcendental entire function in the Eremenko-Lyubich class B. We give a lower bound for the Hausdorff dimension of the Julia set of f that depends on the growth of f . This estimate is best possible and is obtained by proving a more general result concerning the size of the escaping set of a function with a logarithmic tract.

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 2006