Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-02T23:10:52.918Z Has data issue: false hasContentIssue false
  • English
  • Français

Lyapunov optimizing measures for C1 expanding maps of the circle

Published online by Cambridge University Press:  15 October 2008

OLIVER JENKINSON  and
IAN D. MORRIS
OLIVER JENKINSON
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK (email: [email protected])
IAN D. MORRIS
Affiliation:
School of Mathematics, University of Manchester, Sackville Street, Manchester M60 1QD, UK Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (email: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

For a generic C1 expanding map of the circle, the Lyapunov maximizing measure is unique and fully supported, and has zero entropy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 6 , December 2008 , pp. 1849 - 1860
Copyright
Copyright © 2008 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Billingsley, P.. Convergence of Probability Measures, 2nd edn. Wiley, New York, 1999.CrossRefGoogle Scholar
[2] Bousch, T. and Jenkinson, O.. Cohomology classes of dynamically non-negative C k functions. Invent. Math. 148 (2002), 207–217.CrossRefGoogle Scholar
[3] Contreras, G., Lopes, A. and Thieullen, Ph.. Lyapunov minimizing measures for expanding maps of the circle. Ergod. Th. & Dynam. Sys. 21 (2001), 1379–1409.CrossRefGoogle Scholar
[4] Katok, A. and Hasselblatt, B.. Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications, 54). Cambridge University Press, Cambridge, 1995.CrossRefGoogle Scholar
[5] Newhouse, S.. Continuity properties of entropy. Ann. of Math. (2) 129 (1989), 215–235.CrossRefGoogle Scholar
[6] Sigmund, K.. Generic properties of invariant measures for Axiom A diffeomorphisms. Invent. Math. 11 (1970), 99–109.CrossRefGoogle Scholar