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math.DS2009★ 1 cited
Two remarks about Mañé's conjecture
Daniel Massart
We prove that Mañé's conjecture, as stated in {\em Lagrangian flows: the dynamics of globally minimizing orbits}, Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), no. 2, 141--153, contains…
math.DS2009
Differentiability of Mather's beta function in low dimensions
Daniel Massart
Let L be a time-periodic Lagrangian on a two-torus. Then the beta-function of L is differentiable at least in k directions at any k-irrational homology class, for k= 0, 1, 2.
math.DS2009
Differentiability of Mather's average action and integrability on closed surfaces
Daniel Massart, Alfonso Sorrentino
In this article we study the differentiability of Mather's -function on closed surfaces and its relation to the integrability of the system.