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Invariant measures for piecewise linear fractional maps

Part of: Measure-theoretic ergodic theory

Published online by Cambridge University Press:  09 April 2009

F. Schweiger
F. Schweiger
Affiliation:
Department of Mathematics Monash UniversityClayton, Victoria, 3168, Australia Institut für Mathematik Universität SalzburgSalzburg Oesterreich
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Abstract

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Let T: [0,1] → [0,1] be a map which is given piecewise as a linear fractional map such that T0 = T] = 0 and T'0 < 1. Then T is ergodic and admits an invariant measure which can be calculated explicitly.

MSC classification

Secondary: 28D05: Measure-preserving transformations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 1 , February 1983 , pp. 55 - 59
Copyright
Copyright © Australian Mathematical Society 1983

References

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