Embedded continued fractals and their Hausdorff dimension
type: Item
instance of: scholarly article
title: Embedded continued fractals and their Hausdorff dimension
zbMATH Open document ID: 0664.28002
DOI: 10.1007/BF01889601
published in: Constructive Approximation
publication date: 1989-01-01T00:00:00Z
review text: Let \(\alpha\) be irrational and \(g\) be a given monotone decreasing function. A construction is given which attaches to a number \(k\) a polygon \(Q_k\). Under certain hypotheses on \(\alpha\) and \(g\) a subsequence of \((Q_k)\) converges to a continuous limit curve \(Q\). If \(\alpha^2+\alpha N=1\), where \(N\) is an even number, then the curve \(Q\) is embedded for special choices of \(g\) and its Hausdorff dimension can be computed. The main tool is the continued fraction expansion of \(\alpha\) which fact obviously is the reason why the curve \(Q\) is called a ``continued fractal''.
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 4085966
zbMATH Keywords: continuous limit curve
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: continued fraction expansion
zbMATH Keywords: continued fractal
author: Jenny Harrison
reviewed by: Fritz Schweiger
MaRDI profile type: Publication
cites work: Complex analytic dynamics on the Riemann sphere
cites work: Q5772619
cites work: Continued fractals and the Seifert conjecture
cites work: Q3032328
cites work: On a conjecture of Erdös and Szüsz related to uniform distribution mod 1
full work available at URL: https://doi.org/10.1007/bf01889601
OpenAlex ID: W4241044293
description: scientific article; zbMATH DE number 4085966