Geometric properties of the Markov and Lagrange spectra
  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 $[0, 1]$. 
Carlos Gustavo Moreira
math.NT