Scaling Functions for Degree 2 Circle Endomorphisms

نویسندگان

  • G. Cui
  • F. P. Gardiner
  • Y. Jiang
چکیده

We prove that a continuous function on the dual Cantor set is the scaling function of a uniformly symmetric circle endomorphism if and only if it satisfies a summation condition and compatibility condition. We use this result to establish an isomorphism between the space of continuous functions on the dual Cantor set satisfying these conditions and a Teichmüller space.

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

Scaling Functions And Gibbs Measures And Teichmüller Spaces Of Circle Endomorphisms

We study the scaling function of a C1+h expanding circle endomorphism. We find necessary and sufficient conditions for a Hölder continuous function on the dual symbolic space to be realized as the scaling function of a C1+h expanding circle endomorphism. We further represent the Teichmüller space of C1+h expanding circle endomorphisms by the space of Hölder continuous functions on the dual symb...

متن کامل

Function Models for Teichmüller Spaces and Dual Geometric Gibbs Type Measure Theory for Circle Dynamics

Geometric models and Teichmüller structures have been introduced for the space of smooth circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one under the Techmüller metric. Moreover, the spaces of geometric models as well as the Teichmüller spaces can be described as the space of Hölder continuous scaling function...

متن کامل

Circle Endomorphisms, Dual Circles and Thompson’s Group

We construct the dual Cantor set for a degree two expanding map f acting as cover of the circle T onto itself. Then we use the criterion for a continuous function on this Cantor set to be the scaling function of a uniformly asymptotically affine UAA expanding map to show that the scaling function for f descends to a continuous function on a dual circle T∗. We use this representation to view the...

متن کامل

A Characterization of the Uniquely Ergodic Endomorphisms of the Circle

We characterize the uniquely ergodic endomorphisms of the circle in terms of their periodic orbits. Let /: S1 -• S1 be a continuous endomorphism of the circle S1 . Denote by F: R —► R its lifting to the universal covering space. Then, for all x £ R, F satisfies F(x + 1) = F(x) + k for some k £ Z. The number k is called the degree of / (when necessary this number will also be called the degree o...

متن کامل

On Expanding Endomorphisms of the Circle Ii

In this paper we give sufficient conditions for weak isomorphism of Lebesgue measure-preserving expanding endomorphisms of S1.

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 2003