Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping
type: Item
instance of: scholarly article
title: Random mappings with a single absorbing center and combinatorics of discretizations of the logistic mapping
zbMATH Open document ID: 0937.37012
DOI: 10.1155/S1048953399000209
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2000-02-14T00:00:00Z
full work available at URL: https://eudml.org/doc/48411
review text: This paper studies some properties of random mappings with a single absorbing center and applies them to several discretizations of the logistic mapping. In the first part of the paper, after introducing auxiliary notations, the continuous limit of several distributions as well as estimates are proved. Next the authors introduce the concept of absorbing center as a set such that once a trajectory enters this set it cannot leave it, noting that random mappings with an absorbing center are similar to mappings with a single attracting center. Then some results on the distributions of basins of attractions and the cycle lengths are established. Finally these results are applied to discretizations of the logistic map explaining some phenomena that occur in computer simulation of this dynamical system.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 65P20
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 1383841
zbMATH Keywords: random mappings
zbMATH Keywords: discretization of logistic map
zbMATH Keywords: chaotic numerics
zbMATH Keywords: absorbing center
zbMATH Keywords: logistic mapping
zbMATH Keywords: attracting center
zbMATH Keywords: basins of attractions
author: Anthony Klemm
author: Alexei Pokrovskii
reviewed by: Manuel Calvo
MaRDI profile type: Publication
OpenAlex ID: W2103915513
description: scientific article; zbMATH DE number 1383841