# Geometric properties of the Markov and Lagrange spectra

### Abstract

We prove several results on (fractal) geometric properties of the classical Markov and Lagrange spectra. In particular, we prove that the Hausdorff dimensions of intersections of both spectra with half-lines always coincide, and may assume any real value in the interval $[0, 1]$.

## Authors

Carlos Gustavo Moreira

IMPA, Estrada Dona Castorina, 110, Jardim Botânico, CEP 22460 - 320, Rio de Janeiro, Brasil