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arXiv · 1708.06258

$HD(M\setminus L)<0.986927$

Carlos Matheus·Carlos Gustavo Moreira
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Abstract

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

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Carlos Matheus, Carlos Gustavo Moreira. 2017-08-21. $HD(M\setminus L)<0.986927$. https://arxiv.org/abs/1708.06258

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