doi:10.3934/dcds.1999.5.535          Full text: (258.6K)

Guizhen Cui - Institute of Mathematics, Academia Sinica, Beijing 100080, China (email)

Yunping Jiang - Department of Mathematics, Queens College of CUNY, Flushing, NY 11367, United States (email)

Anthony Quas - Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States (email)

Abstract: We study the scaling function of a $C^{1+h}$ 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 $C^{1+h}$ expanding circle endomorphism. We further represent the Teichmüller space of $C^{1+h}$ 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.

Keywords: Scaling function, g-measure, Teichmüller space.
Mathematics Subject Classification: 58F23, 30C62.

Received:  October   1997
Revised:   March  1999
Published: May  1999

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