Distribution of iterates of first order difference equations
JB McGuire, CJ Thompson
Bulletin of the Australian Mathematical Society | Published : 1980
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.