%0 Journal Article %A Sorrentino, A. %A Veselov, Alexander %D 2019 %T Markov numbers, Mather's beta-function and stable norm %U https://repository.lboro.ac.uk/articles/journal_contribution/Markov_numbers_Mather_s_beta-function_and_stable_norm/9376616 %2 https://repository.lboro.ac.uk/ndownloader/files/16987958 %K untagged %K Mathematical Sciences not elsewhere classified %X V. Fock [7] introduced an interesting function ψ(x), x ∈ R related to Markov numbers. We explain its relation to Federer-Gromov’s stable norm and Mather’s β-function, and use this to study its properties. We prove that ψ and its natural generalisations are differentiable at every irrational x and non-differentiable otherwise, by exploiting the relation with length of simple closed geodesics on the punctured or oneholed tori with the hyperbolic metric and the results by Bangert [3] and McShane-Rivin [23]. %I Loughborough University