Asymptotic periodicity of the iterates of weakly constrictive Markov operators
type: Item
instance of: scholarly article
title: Asymptotic periodicity of the iterates of weakly constrictive Markov operators
zbMATH Open document ID: 0578.47020
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: A Markov operator \(P: L^ 1\to L^ 1\) is said weakly constrictive if there exists a weakly compact set \(f\subset L^ 1\) which is an attractor for trajectories \(p^ nf\) of all densities \(f\in L^ 1\). This property is proved to be a sufficient condition for asymptotic periodicity of all \(p^ nf\), \(f\in L^ 1\). It is a generalization of the main result of [\textit{A. Lasota}, \textit{T. Y. Li} and \textit{J. A. Yorke}, Trans. Am. Math. Soc. 286, 751-764 (1984; Zbl 0564.47015)], where strong constrictivity is assumed.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 47B40
zbMATH DE Number: 3925629
zbMATH Keywords: Markov operator
zbMATH Keywords: weakly constrictive
zbMATH Keywords: attractor for trajectories
zbMATH Keywords: asymptotic periodicity
author: Jozef Komorník
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228533
OpenAlex ID: W2098403143
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DOI: 10.2748/TMJ/1178228533
description: scientific article; zbMATH DE number 3925629