We study the action functional associated to a smooth Lagrangian function on the tangent
bundle of a manifold, having quadratic growth in the velocities. We show that, although the …

We study singularities of Lagrangian mean curvature flow in ℂ n when the initial condition is
a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are …

Let \BbbL be a convex superlinear Lagrangian on a closed connected manifold N. We
consider critical values of Lagrangians as defined by R. Mañé in M3. We show that the …

Let, a quantity, The asymptotic Maslov index, which describes the way Lagrangian planes
are asymptotically wrapped in average around the Lagrangian Grassmann bundle. We pay …

The objective of this note is to present some results, to be proved in a forthcoming paper,
about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our …

After reviewing some classical results about hyperbolic dynamics in a Banach setting, we
describe the Morse complex for gradient-like flows on an infinite-dimensional Banach …

The symplectic action can be defined on the space of smooth paths in a symplectic manifold
P which join two Lagrangian submanifolds of P. To pursue a new approach to the variational …

Unlike the classical (first-order) energy of a curve in a Riemannian manifold, the bending
energy (total squared curvature) of an immersed curve does not directly induce a …

On a smooth, compact and oriented manifold without boundary, we give a complete
description of the correlation function of a Morse-Smale gradient flow satisfying a certain …

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 …