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Coboundary equations of eventually expanding transformations

Published online by Cambridge University Press:  17 April 2009

Young-Ho Ahn
Young-Ho Ahn
Affiliation:
School of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea, e-mail: ahn@euclid.kaist.ac.kr
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Abstract

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Let T be an eventually expansive transformation on the unit interval satisfying the Markov condition. The T is an ergodic transformation on (X, ß, μ) where X = [0, 1), ß is the Borel σ-algebra on the unit interval and μ is the T invariant absolutely continuous measure. Let G be a finite subgroup of the circle group or the whole circle group and φ: X → G be a measurable function with finite discontinuity points. We investigate ergodicity of skew product transformations Tφ on X × G by showing the solvability of the coboundary equation φ(x) g (Tx) = λg (x), |λ| = 1. Its relation with the uniform distribution mod M is also shown.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 39 - 50
Copyright
Copyright © Australian Mathematical Society 2003

References

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