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 we may assume any real value in the interval $[0, 1]$.

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Authors

Carlos Gustavo Moreira

Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil