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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2010 | 210 | 1 | 47-62

## The absolute continuity of the invariant measure of random iterated function systems with overlaps

EN

### Abstrakty

EN
We consider iterated function systems on the interval with random perturbation. Let $Y_ε$ be uniformly distributed in [1-ε,1+ ε] and let $f_i ∈ C^{1+α}$ be contractions with fixpoints $a_i$. We consider the iterated function system ${Y_{ε}f_{i} + a_{i}(1-Y_{ε})}ⁿ_{i=1}$, where each of the maps is chosen with probability $p_i$. It is shown that the invariant density is in L² and its L² norm does not grow faster than 1/√ε as ε vanishes. The proof relies on defining a piecewise hyperbolic dynamical system on the cube with an SRB-measure whose projection is the density of the iterated function system.

47-62

wydano
2010

### Twórcy

autor
• Department of Stochastics, Institute of Mathematics, Technical University of Budapest, P.O. Box 91, 1521 Budapest, Hungary
autor
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland