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Iteration of piecewise linear maps on an interval

Published online by Cambridge University Press:  17 April 2009

James B. McGuire  and
Colin J. Thompson
James B. McGuire
Affiliation:
Professor James B. McGuire, Department of Physics, Florida Atlantic University, Boca Raton, Florida 33432, USA;
Colin J. Thompson
Affiliation:
Professor Colin J. Thompson, School of Natural Sciences, The Institute for Advanced Study, Princeton, New Jersey 08540, USA;
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Abstract

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A complete analysis is given of the iterative properties of two piece-piecewise linear maps on an interval, from the point of view of a doubling transformation obtained by functional composition and rescaling. We show how invariant measures may be constructed for such maps and that parameter values where this may be done form a dense set in a one-dimensional subset of parameter space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 3 , December 1981 , pp. 433 - 451
Copyright
Copyright © Australian Mathematical Society 1981

References

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