English

$HD(M\setminus L)<0.986927$

Dynamical Systems 2019-10-04 v3

Abstract

We show that several portions of the complement MLM\setminus L of the Lagrange spectrum LL in the Markov spectrum MM can be seen as subsets of arithmetic sums of Cantor sets with controlled Hausdorff dimensions. In particular, we prove that MLM\setminus L has Hausdorff dimension strictly smaller than one.

Keywords

Cite

@article{arxiv.1708.06258,
  title  = {$HD(M\setminus L)<0.986927$},
  author = {Carlos Matheus and Carlos Gustavo Moreira},
  journal= {arXiv preprint arXiv:1708.06258},
  year   = {2019}
}

Comments

16 pages, no figures. This preprint became a portion of the latest version of arXiv:1803.01230 and, for this reason, we are withdrawing it

R2 v1 2026-06-22T21:19:38.637Z