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arXiv 1708.06258math.DS
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$HD(M\setminus L)<0.986927$

$HD(M\setminus L)<0.986927$

Carlos Matheus, Carlos Gustavo Moreira

备注：
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
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摘要：

我们表明，补充$M\setminus L$的拉格朗日谱$L$在马尔可夫谱$M$的几个部分可以看作是康托集的算术和控制豪斯多夫维数的子集。特别地，我们证明了$M\setminus L$的豪斯多夫维数严格小于1.

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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