%0 Journal Article %T Differentiability of Mather's average action and integrability on closed surfaces %A Daniel Massart %A Alfonso Sorrentino %J Mathematics %D 2009 %I arXiv %X In this article we study the differentiability of Mather's $\beta$-function on closed surfaces and its relation to the integrability of the system. %U http://arxiv.org/abs/0907.2055v2