Geometric properties of the Markov and Lagrange spectra

By Carlos Gustavo T. de A. Moreira. Annals of Mathematics, 2016

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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 $[0, 1]$.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cdda338dab8214048c7dda2291b7339c3782fe70