41 citations · 250 across the 50 of their papers we have counts for
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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…
New gaps on the Lagrange and Markov spectra
Luke Jeffreys, Carlos Matheus, Carlos Gustavo Moreira
Let and denote the Lagrange and Markov spectra, respectively. It is known that and that . In this work, we exhibit new gaps of …
Diophantine approximations, Markov and Lagrange spectra and dynamical Cantor sets
Carlos Matheus, Carlos Gustavo Moreira
This text is a slightly expanded version of a survey article on certain aspects of low dimensional dynamics and number theory written after a kind invitation by the editors of the…
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…
is not closed
Davi Lima, Carlos Matheus, Carlos Gustavo Moreira +1
We show that is a point of the Lagrange spectrum which is accumulated by a sequence of elements of the complement of the Lagrange spectrum in the…
near 3
Davi Lima, Carlos Matheus, Carlos Gustavo Moreira +1
We construct four new elements of lying in distinct connected components of , where is the Markov spectrum and …