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  • Ergodic Theory and Dynamical Systems, Volume 5, Issue 2
  • June 1985, pp. 285-289

Expanding endomorphisms of the circle revisited

  • Michael Shub (a1) and Dennis Sullivan (a2)
  • DOI:
  • Published online: 01 September 2008

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.

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[2]N. F. G. Martin . On finite Blaschke products whose restriction to the unit circle are exact endomorphisms. Bull. London Math. Soc. 15 (1983), 343348.

[4]W. Parry & P. Walters . Endomorphisms of a Lebesgue space. Bull. Amer. Math. Soc. (1972), 272276.

[8]P. Walters . Invariant measures and equilibrium states for some mappings which expand distances. Trans. Amer. Math. Soc. 236 (1978), 121153.

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