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arXiv · 1904.00269

$M\setminus L$ near 3

Davi Lima·Carlos Matheus·Carlos Gustavo Moreira·Sandoel Vieira
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Abstract

We construct four new elements $3.11>m_1>m_2>m_3>m_4$ of $M\backslash L$ lying in distinct connected components of $\mathbb{R}\setminus L$, where $M$ is the Markov spectrum and $L$ is the Lagrange spectrum. These elements are part of a decreasing sequence $(m_k)_{k\in\mathbb{N}}$ of elements in $M$ converging to $3$ and we give some evidence towards the possibility that $m_k\in M\setminus L$ for all $k\geq 1$. In particular, this indicates that $3$ might belong to the closure of $M\setminus L$, so that the answer to Bousch's question about the closedness of $M\setminus L$ might be negative.

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Davi Lima, Carlos Matheus, Carlos Gustavo Moreira, Sandoel Vieira. 2019-03-30. $M\setminus L$ near 3. https://arxiv.org/abs/1904.00269

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