Daniel Massart

On Aubry sets and Mather’s action functional

We study Lagrangian systems on a closed manifoldM. We link the differentiability of Mather’sβ-function with the topological complexity of the complement of the Aubry set. As a consequence, whenM is a closed, orientable surface, the differentiability of theβ-function at a given homology class is forced by the irrationality of the homology class. This allows us to prove the two-dimensional case of a conjecture by Mañé.

Differentiability of Mather's average action and integrability on closed surfaces

In this article we study the differentiability of Mathers

Aubry sets vs. Mather sets in two degrees of freedom

\beta

Vertices of Mather’s beta function, II

-function on closed surfaces and its relation to the integrability of the system.

Subsolutions of time-periodic Hamilton–Jacobi equations

Let L be an autonomous Tonelli Lagrangian on a closed manifold of dimension two. We prove that for a large set of cohomology classes, the Aubry set consists of periodic orbits.

Mañé's conjectures in codimension 1

If the

Ma\~n\'e's conjectures in codimension one

\beta

On the intersection form of surfaces

-function of a time-periodic Lagrangian on a manifold

Two remarks about Mañé’s conjecture

M

Erratum to “On Aubry sets and Mather’s action functional”

has a vertex at a