$M\backslash L$ is not closed

Davi Lima; Carlos Matheus; Carlos Gustavo Moreira; Sandoel Vieira

$M\backslash L$ is not closed

Number Theory 2020-04-09 v2

Authors: Davi Lima , Carlos Matheus , Carlos Gustavo Moreira , Sandoel Vieira

Abstract

We show that $1+3/\sqrt{2}$ is a point of the Lagrange spectrum $L$ which is accumulated by a sequence of elements of the complement $M\setminus L$ of the Lagrange spectrum in the Markov spectrum $M$ . In particular, $M\setminus L$ is not a closed subset of $\mathbb{R}$ , so that a question by T. Bousch has a negative answer.

Cite

@article{arxiv.1912.02698,
  title  = {$M\backslash L$ is not closed},
  author = {Davi Lima and Carlos Matheus and Carlos Gustavo Moreira and Sandoel Vieira},
  journal= {arXiv preprint arXiv:1912.02698},
  year   = {2020}
}

Comments

33 pages, to appear in Int. Math. Res. Notices

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