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Moscow Mathematical Journal

Volume 21, Issue 4, October–December 2021  pp. 767–788.

ML Near 3

Authors:  Davi Lima (1), Carlos Matheus (2), Carlos Gustavo Moreira (3), and Sandoel Vieira (3)
Author institution:(1) Instituto de Matemática, UFAL, Av. Lourival Melo Mota s/n, Maceio, Alagoas, Brazil
(2) CMLS, École Polytechnique, CNRS (UMR 7640), 91128, Palaiseau, France
(3) IMPA, Estrada Dona Castorina, 110. Rio de Janeiro, Rio de Janeiro-Brazil


Summary: 

We construct four new elements 3.11>m1>m2>m3>m4 of ML lying in distinct connected components of RL, where M is the Markov spectrum and L is the Lagrange spectrum. These elements are part of a decreasing sequence (mk)kN of elements in M converging to 3 and we give some evidence towards the possibility that mkML for all k1. In particular, this indicates that 3 might belong to the closure of ML. So, ML would not be closed near 3 and there would not exist ε>0 such that M(,3+ε)=L(,3+ε).

2020 Math. Subj. Class. 11A55, 11J06.



Keywords: Markov spectrum, Lagrange spectrum, Diophantine approximation.

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