Continued fractions as dynamical systems
type: Item
instance of: scholarly article
title: Continued fractions as dynamical systems
zbMATH Open document ID: 1383.37005
author: Felice Iavernaro
author: Donato Trigiante
published in: Applied Mathematics and Computation
publication date: 2012-08-19T00:00:00Z
review text: In the paper under review, the authors study a dynamical systems approach to continued fractions. It is well-known that there is an interpretation of the continued fraction expansion process as a discrete two-dimensional dynamical system. On the contrary, in the present paper the authors study a new three-dimensional dynamical system which can be used to model the continued fraction expansion of quadratic irrationals, by this means continuing their research from [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e2136--e2151 (2009; Zbl 1239.11009)]. Simply speaking, the three-dimensional points correspond to the coefficients of quadratic polynomials, which result from the continued fraction algorithm. After studying the properties of such dynamical systems, the paper is concluded with a section discussing the connection of these results with the solutions of certain Pell equations.
reviewed by: Christoph Aistleitner
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 39A60
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 40A15
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11D09
zbMATH DE Number: 6068267
zbMATH Keywords: continued fractions
zbMATH Keywords: discrete dynamical systems
zbMATH Keywords: quadratic irrationals
zbMATH Keywords: Pell equations
MaRDI profile type: Publication
full work available at URL: j.amc.2011.02.092
OpenAlex ID: W2029948350
cites work: Pell's equation
cites work: Polynomial roots: The ultimate answer?
cites work: Q3996883
cites work: Continued fractions without fractions: Lagrange theorem and Pell equations
cites work: Continued fractions with even period and an infinite family of real quadratic fields of minimal type
cites work: Q4531875
cites work: Q5736199
cites work: Continued fraction gems
cites work: Difference equations and continued fractions
cites work: Q3312297
cites work: Efficient strategy for adaptive partition of N-dimensional intervals in the framework of diagonal algorithms
DOI: 10.1016/J.AMC.2011.02.092
description: scientific article; zbMATH DE number 6068267