Approximation of the Lagrange and Markov spectra

08/10/2019

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by   Vincent Delecroix, et al.

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The (classical) Lagrange spectrum is a closed subset of the positive real numbers defined in terms of diophantine approximation. Its structure is quite involved. This article describes a polynomial time algorithm to approximate it in Hausdorff distance. It also extends to approximate the Markov spectrum related to infimum of binary quadratic forms.