SORRENTINO, A. and VESELOV, A.P., 2019. Markov numbers, Mather's beta-function and stable norm. Nonlinearity, In Press.
V. Fock  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  and
This paper is in closed access until it is published.