Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
47-62
Opis fizyczny
Daty
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
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm210-1-2