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Distribution of iterates of first order difference equations

Published online by Cambridge University Press:  17 April 2009

James B. McGuire  and
Colin J. Thompson
James B. McGuire
Affiliation:
Department of Physics, Florida Atlantic University, Boca Raton, Florida 33432, USA
Colin J. Thompson
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia.
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Abstract

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An invariant measure which is absolutely continuous with respect to Lebesgue measure is constructed for a particular first order difference equation that has an extensive biological pedigree. In a biological context this invariant measure gives the density of the population whose growth is governed by the difference equation. Further asymptotically universal results are obtained for a class of difference equations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 1 , August 1980 , pp. 133 - 143
Copyright
Copyright © Australian Mathematical Society 1980

References

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