Mathematics – Dynamical Systems
Scientific paper
2009-03-12
Mathematics
Dynamical Systems
14 pages
Scientific paper
We consider iterated function systems on the interval with random perturbation. 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 $L^2$-norm does not grow faster than $1/\sqrt{\epsilon}$, as $\epsilon$ vanishes.
Barany Balazs
Persson Tomas
No associations
LandOfFree
The absolute continuity of the invariant measure of random iterated function systems with overlaps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The absolute continuity of the invariant measure of random iterated function systems with overlaps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The absolute continuity of the invariant measure of random iterated function systems with overlaps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-36527