  V. Fock [7] introduced an interesting function $\psi(x)$, $x \in {\mathbb R}$
related to Markov numbers. We explain its relation to Federer-Gromov's stable
norm and Mather's $\beta$-function, and use this to study its properties. We
prove that $\psi$ and its natural generalisations are differentiable at every
irrational $x$ and non-differentiable otherwise, by exploiting the relation
with length of closed geodesics on the punctured or one-hole tori with the
hyperbolic metric and the results by Bangert [3] and McShane- Rivin [19].
