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Abstract: We consider iterated function systems on the interval with randomperturbation. Let $Y \epsilon$ be uniformly distributed in $1- \epsilon, 1 +\epsilon$ and let $f i \in C^{1+\alpha}$ be contractions with fixpoints $a i$.We consider the iterated function system $\{Y \epsilon f i + a i 1 -Y \epsilon \} {i=1}^n$, were each of the maps are chosen with probability$p i$. It is shown that the invariant density is in $L^2$ and the $L^2$-normdoes not grow faster than $1-\sqrt{\epsilon}$, as $\epsilon$ vanishes.



Autor: Balazs Barany, Tomas Persson

Fuente: https://arxiv.org/







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