John Mather's seminal works in Hamiltonian dynamics represent some of the most important
contributions to our understanding of the complex balance between stable and unstable …

The aim of these notes is to present a self contained account of discrete weak KAM theory.
Put aside the intrinsic elegance of this theory, it is also a toy model for classical weak KAM …

These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and
Hamiltonian systems. They are based on a series of lectures given by the author at …

On the Hausdorff dimension of the mather quotient Page 1 On the Hausdorff Dimension of the
Mather Quotient ALBERT FATHI Unité de Mathématiques Pures et Appliquées ALESSIO …

arXiv:0907.2055v2 [math.DS] 9 Dec 2010 Page 1 arXiv:0907.2055v2 [math.DS] 9 Dec 2010
Differentiability of Mather’s average action and integrability on closed surfaces Daniel Massart …

The Monge transportation problem is more than 200 years old [110], and it has generated in
the last years a huge amount of work. Originally Monge wanted to move, in 3-space, a …

In the context of Mather's theory of Lagrangian systems, we study the decomposition in chain-
transitive classes of the Mather invariant sets. As an application, we prove, under …

Given a Tonelli Hamiltonian H: T* M→ ℝ of class Ck, with k≥ 2, we prove the following
results:(1) Assume there exist a recurrent point of the projected Aubry set and a critical …

Let $(M, g) $ be a closed, connected and orientable Riemannian manifold with nonnegative
Ricci curvature. Consider a Lagrangian $ L (x, v): TM\to\R $ defined by $ L (x, v):=\frac 12g_x …

Dynamic and asymptotic behavior of singularities of certain weak KAM solutions on the torus -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …