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Invariant measures for families of circle maps

Published online by Cambridge University Press:  24 October 2008


Anthony Quas
Affiliation:
Mathematics institute, University of Warwick, Coventry, CV4 7AL

Abstract

In this paper, we establish conditions for a continuous family of circle maps to have a continuous family of invariant measures in the appropriate topologies, and demonstrate the necessity of some of the conditions.


Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

[1]Baker, A.. A Concise introduction to the Theory of Numbers (Cambridge University Press, 1984).CrossRefGoogle Scholar
[2]Cornfeld, I. P., Fomin, S. V. and Sinai, Ya. G.. Ergodic Theory (Springer-Verlag, 1982).CrossRefGoogle Scholar
[3]Herman, M. R.. Sur la conjugaison differentiable des diffeomorphismes du cercie à des rotations. Inst. Hautes Études Sci. Publ. Math. 49 (1979), 5233.CrossRefGoogle Scholar
[4]Walters, P.. An Introduction to Ergodic Theory (Springer-Verlag, 1981).Google Scholar

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