On the condensation points of the Lagrange spectrum
type: Item
instance of: scholarly article
title: On the condensation points of the Lagrange spectrum
zbMATH Open document ID: 0638.10033
DOI: 10.1007/BF02843911
author: Marco Pavone
publication date: 1986-01-01T00:00:00Z
review text: Let \(\alpha =[a_ 0;a_ 1,a_ 2,...]\) be the simple continued fraction expansion of \(\alpha\). If \(M=\{...,a_{-1},a_ 0,a_ 1,...\}\) is a sequence of positive integers \(a_ k\), then \[ \limsup_{k\to \pm \infty}([a_ k;a_{k+1},a_{k+2},...]+[0;a_{k-1},a_{k-2},...]) \] is called Lagrange value of M and the set of all such values is called Lagrange spectrum L. Let L(N) be the Lagrange spectrum of the Lagrange values of all sequences M, for which \(a_ k\leq N\) \((a_ k=N\) infinitely many times), where N is an arbitrary positive integer. Many authors have studied the condensation points of L and L(N). The author of the present paper proves a theorem for the constructing such points of L(N). The proof is based on a similar theorem about L, given by \textit{M. E. Gbur} [Monatsh. Math. 84, 91-108 (1977; Zbl 0372.10019)].
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 11J04
zbMATH DE Number: 4040005
zbMATH Keywords: simple continued fraction expansion
zbMATH Keywords: Lagrange spectrum
zbMATH Keywords: condensation points
reviewed by: Tonko Tonkov
MaRDI profile type: Publication
cites work: Q4116521
cites work: Accumulation points of the Lagrange and Markov spectra
cites work: Q3244174
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4040005