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

• Autorzy: Balázs Bárány , Tomas Persson
• Języki publikacji: 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.

Kategorie tematyczne

• 37C40: Smooth ergodic theory, invariant measures
• 37H15: Multiplicative ergodic theory, Lyapunov exponents

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 210
• Numer: 1
• Strony: 47-62

Daty

wydano

2010

Twórcy

autor

Balázs Bárány

• Department of Stochastics, Institute of Mathematics, Technical University of Budapest, P.O. Box 91, 1521 Budapest, Hungary

autor

Tomas Persson

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm210-1-2