Expanding endomorphisms of the circle revisited

Abstract

Abstract Two C r , r ≥ 2, expanding maps of the circle which are absolutely continuously conjugate are C r conjugate. Here ƒ and g : S 1 → S 1 are expanding if they stretch tangent vectors in some metric, and a conjugacy is an isomorphism h : S 1 → S 1 such that fh = hg .