The lagrange and markov spectra from the dynamical point of view

Abstract

This text grew out of my lecture notes for a 4-h minicourse delivered on October 17 and 19, 2016 during the research school “Applications of Ergodic Theory in Number Theory”—an activity related to the Jean-Molet Chair project of Mariusz Lemańczyk and Sébastien Ferenczi—realized at CIRM, Marseille, France. The subject of this text is the same as my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with a special emphasis on a recent theorem of C.G. Moreira).