Abstract
We study the scaling function of a $C^{1+h}$ expanding circle endomorphism. We find necessary and sufficient conditions for a Holder continuous function on the dual symbolic space to be realized as the scaling function of a $C^{1+h}$ expanding circle endomorphism. We further represent the Teichmuller space of $C^{1+h}$ expanding circle endomorphisms by the space of Holder continuous functions on the dual symbolic space satisfying our necessary and sufficient conditions and study the completion of this Teichmuller space in the universal Teichmuller space.
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