Iteration of Möbius transformations and attractors on the real line
type: Item
instance of: scholarly article
title: Iteration of Möbius transformations and attractors on the real line
zbMATH Open document ID: 0878.58041
DOI: 10.1016/S0898-1221(96)00215-5
publication date: 1997-04-17T00:00:00Z
review text: Let \(x_0\) be an arbitrary point in the complex plane. For each positive integer \(n\) the authors choose \(s_n(z)\) to be \(-5/(1+z)\) or \(-0.5/(1+z)\) with equal probability. They introduce the orbit \((z_n)^\infty_0\), where \(z_n= s_n(z_{n-1})\) for \(n\geq 1\). The authors prove that with probability one the orbit is attracted to the real axis.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 30C20
zbMATH DE Number: 1001341
zbMATH Keywords: Möbius transformation
zbMATH Keywords: Markov process
zbMATH Keywords: continued fraction
author: Anders Barrlund
author: Hans Wallin
author: Johan Karlsson
reviewed by: Yoshihide Kozai
MaRDI profile type: Publication
cites work: Iteration of Möbius transforms and continued fractions
cites work: Q4295468
cites work: Q4040874
cites work: Q3889331
cites work: Noncommuting Random Products
cites work: Q3741845
full work available at URL: s0898-1221(96)00215-5
OpenAlex ID: W2027452257
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 1001341