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A Bound on the Number of Invariant Measures

Published online by Cambridge University Press:  20 November 2018

Abraham Boyarsky
Abraham Boyarsky*
Affiliation:
Department of Mathematics, Sir George Williams Campus, Concordia University, Montreal, Canada
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For τ a piecewise C2 transformation, we present a method for obtaining an upper bound for the number of independent absolutely continuous measures invariant under τ.

Let τ = [0,1] and let τ:I→ J be a piecewise C2 transformation with infI1 |dτ/dx| > 1, where I1 = I-P and P denotes the points of discontinuity of τ and τ′

Keywords

28DOS
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 123 - 124
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Lasota, A. and Yorke, J. A., On the existence of invariant measures for piecewise monotonie transformations, Trans. Amer. Math. Soc. 186 (1962), 481-488.Google Scholar
2. Li, T.Y. and Yorke, J. A., Ergodic transformations from an interval into itself, Trans. Amer. Math. Soc. 235 (1962), 183-192.Google Scholar