At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

We consider (M, d) a connected and compact manifold and we denote by the Bernoulli
space Mℤ. The analogous problem on the half-line ℕ is also considered. Let be an …

We propose a PDE approach to the Aubry-Mather theory using viscosity solutions. This
allows to treat Hamiltonians (on the flat torus T^N) just coercive, continuous and …

We consider a continuous coercive Hamiltonian H on the cotangent bundle of the compact
connected manifold M which is convex in the momentum. If u_ λ: M → R u λ: M→ R is the …

This paper, building upon ideas of Mather, Moser, Fathi, E and others, applies PDE (partial
differential equation) methods to understand the structure of certain Hamiltonian flows. The …

Given a normally hyperbolic invariant manifold Λ for a map f, whose stable and unstable
invariant manifolds intersect transversally, we consider its associated scattering map. That …

New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years,
gave deep insight into the dynamics of convex Lagrangian systems. This book shows how …

Entropy and variational principle for one-dimensional lattice systems with a general a priori
probability: positive and zero tem Page 1 Ergod. Th. & Dynam. Sys. (2015), 35, 1925–1961 …

We consider the Hamilton--Jacobi equation \partial_tu+H(x,Du)=0\qquadin (0,+ ∞) *\T^ N ,
where \T^N is the flat N-dimensional torus, and the Hamiltonian H(x,p) is assumed …

This paper describes the connections between the notions of Hamiltonian system, contact
Hamiltonian system and nonholonomic system from the perspective of differential equations …