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math.NT2022
On the graph of the dimension function of the Lagrange and Markov spectra
Carlos Matheus, Carlos Gustavo Moreira, Polina Vytnova
We study the graph of the function encoding the Hausdorff dimensions of the classical Lagrange and Markov spectra with half-infinite lines of the form . For th…
math.NT2021
Hausdorff dimension of Gauss--Cantor sets and two applications to classical Lagrange and Markov spectra
Carlos Matheus, Carlos Gustavo Moreira, Mark Pollicott +1
This paper is dedicated to the study of two famous subsets of the real line, namely Lagrange spectrum and Markov spectrum . Our first result, Theorem 2.1, provides a rigorou…