Ergodic Theory and Dynamical Systems

Research Article

Expanding endomorphisms of the circle revisited

Michael Shuba1 and Dennis Sullivana2

a1 Department of Mathematics, Queens College and the Graduate School of CUNY, 33 West 42nd Street, New York, NY10036, USA

a2 IHES, 35 Rue de Chartres, 91440 Bures-sur-Yvette, France

Abstract

Two Cr, r ≥ 2, expanding maps of the circle which are absolutely continuously conjugate are Cr conjugate. Here ƒ and g: S1S1 are expanding if they stretch tangent vectors in some metric, and a conjugacy is an isomorphism h: S1S1 such that fh = hg.

(Received January 12 1984)

(Revised October 08 1984)