Hostname: page-component-5cf477f64f-r2nwp Total loading time: 0 Render date: 2025-04-04T00:11:50.028Z Has data issue: false hasContentIssue false
  • English
  • Français

Expanding endomorphisms of the circle revisited

Published online by Cambridge University Press:  19 September 2008

Michael Shub  and
Dennis Sullivan
Michael Shub
Affiliation:
Department of Mathematics, Queens Collegeand the Graduate School of CUNY, 33 West 42nd Street, New York, NY10036, USA
Dennis Sullivan
Affiliation:
IHES, 35 Rue de Chartres, 91440 Bures-sur-Yvette, France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Two Cr, r ≥ 2, expanding maps of the circle which are absolutely continuously conjugate are Cr conjugate. Here ƒ and g: S1 → S1 are expanding if they stretch tangent vectors in some metric, and a conjugacy is an isomorphism h: S1 → S1 such that fh = hg.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 285 - 289
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Krzyzewsky, K.. Some results on expanding mappings. Asterisque 50 (1977), 205–218.Google Scholar
[2]Martin, N. F. G.. On finite Blaschke products whose restriction to the unit circle are exact endomorphisms. Bull. London Math. Soc. 15 (1983), 343–348.CrossRefGoogle Scholar
[3]Parry, W.. Entropy and Generators in Ergodic Theory. Benjamin, 1969.Google Scholar
[4]Parry, W. & Walters, P.. Endomorphisms of a Lebesgue space. Bull. Amer. Math. Soc. (1972), 272–276.CrossRefGoogle Scholar
[5]Sacksteder, R.. The measures invariant under an expanding map. In Geometrie Differentielle, Springer Lecture Notes, 392, Springer-Verlag: Berlin; pp. 179–194.Google Scholar
[6]Shub, M.. Endomorphisms of compact differentiable manifolds. Amer. J. Math XCI (1969), 175–199.CrossRefGoogle Scholar
[7]Walters, P.. Some results on the classification of measure preserving transformations. In Recent Advances in Topological Dynamics. Lecture Notes in Math. Vol. 319, pp. 255–276. Springer-Verlag, 1973.Google Scholar
[8]Walters, P.. Invariant measures and equilibrium states for some mappings which expand distances. Trans. Amer. Math. Soc. 236 (1978), 121–153.CrossRefGoogle Scholar