Scaling Functions And Gibbs Measures And Teichmüller Spaces Of Circle Endomorphisms
نویسندگان
چکیده
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 symbolic space satisfying our necessary and sufficient conditions and study the completion of this Teichmüller space in the universal Teichmüller space.
منابع مشابه
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...
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