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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: omj@maths.qmul.ac.uk)
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: ian.morris@warwick.ac.uk)
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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

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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