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β-transformation, invariant measure and uniform distribution

Published online by Cambridge University Press:  09 April 2009

Gavin Brown
Affiliation:
Vice-Chancellor, The University of Sydney, NSW 2006, Australia
Qinghe Yin
Affiliation:
School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia
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Abstract

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Let Tβ be the β-transformation on [0, 1). When β is an integer Tβ is ergodic with respect to Lebesgue measure and almost all orbits {} are uniformly distributed. Here we consider the non-integer case, determine when Tα, Tβ have the same invariant measure and when (appropriately normalised) orbits are uniformly distributed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

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