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

• Autorzy: Zaharopol R.
• 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

EN

attractive probabilities; Dini condition; iterated function systems; Lyapunov functions; Markov operators

PL

funkcja Lapunowa; operator Markowa; prawdopodobieństwo atraktywne; układ funkcji iterowany; warunek Diniego

• 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.