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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-BAT2-0001-0713

Czasopismo

Bulletin of the Polish Academy of Sciences. Mathematics

Tytuł artykułu

Iterated function systems generated by strict contractions and place-dependent probabilities

Autorzy Zaharopol, R. 
Treść / Zawartość http://www.impan.pl/en/publishing-house/journals-and-series/bulletin-polish-acad-sci-math
Warianty tytułu
Języki publikacji EN
Abstrakty
EN Let (w[sub l], w[sub 2],...,w[sub k];p[sub 1],p[sub 2],...p[sub k]) be an iterated function system (IFS for short) with continuous place-dependent probabilities, defined on a metric space (X, d). Assume that every closed ball in X is compact. Our main result is that the IFS has an attractive probability measure whenever the following three conditions are satisfied: (1) w[sub i] : X --> X is a strict contraction for every i = 1,...,k. (2) sum[...]p[sub i](x)p[sub i](y) > 0 for every x, y [belongs to] X. (3) There exists p > 0 in R such that [...] for every x, y [belongs to] X and j = l, 2,...,k. Note that we do not require the p[sub i]'s to be even uniformly continuous. This research was motivated by a question of Barnsley, Demko, Elton, and Geronimo, [1, p. 373], concerning IFS which satisfy only condition (1). We construct a family C of IFS which we use to answer the question. Our main result allows us to distinguish IFS in C which possess attractive probabilities.
Słowa kluczowe
PL funkcja Lapunowa   operator Markowa   prawdopodobieństwo atraktywne   układ funkcji iterowany   warunek Diniego  
EN attractive probabilities   Dini condition   iterated function systems   Lyapunov functions   Markov operators  
Wydawca Instytut Matematyczny PAN
Czasopismo Bulletin of the Polish Academy of Sciences. Mathematics
Rocznik 2000
Tom Vol. 48, no 4
Strony 429--438
Opis fizyczny Bibliogr. 4 poz.,
Twórcy
autor Zaharopol, R.
Bibliografia
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-article-BAT2-0001-0713
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