A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied on each iteration of the process. We study random maps with position dependent probabilities on the interval and on a bounded domain of ℝⁿ. Sufficient conditions for the existence of an absolutely continuous invariant measure for a random map with position dependent probabilities on the interval and on a bounded domain of ℝⁿ are the main results.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-3-5,
author = {Wael Bahsoun and Pawe\l\ G\'ora},
title = {Position dependent random maps in one and higher dimensions},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {271-286},
zbl = {1058.37002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-3-5}
}
Wael Bahsoun; Paweł Góra. Position dependent random maps in one and higher dimensions. Studia Mathematica, Tome 166 (2005) pp. 271-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-3-5/