# The Lagrange and Markov spectra from the dynamical point of view

## TL;DR

This paper explores the structure of the Lagrange and Markov spectra from a dynamical systems perspective, emphasizing recent developments and theorems in the field, particularly those by C. G. Moreira.

## Contribution

It provides a dynamical viewpoint on the Lagrange and Markov spectra, highlighting recent theorems and structural insights in the context of ergodic theory and number theory.

## Key findings

- Analysis of the structure of Lagrange and Markov spectra
- Discussion of recent theorems by C. G. Moreira
- Connection between spectra and dynamical systems

## Abstract

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