This is a tutorial on some of the main ideas in KAM theory. The goal is to present the
background and to explain and compare somewhat informally some of the main methods of …

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 …

We consider the set of maps f\in\mathcal {F} _ {\alpha+}=\cup_ {\beta>\alpha}\mathcal
{C}^{1+\beta} of the circle which are covering maps of degree D, expanding,\min_ {x\in S^ 1} …

Global Minimizers of Autonomous Lagrangians Page 1 Global Minimizers of Autonomous
Lagrangians Gonzalo Contreras Renato Iturriaga cimat mexico, gto. c 2000 Page 2 ii ii Page 3 …

We continue our study of the weak KAM theorem, which we obtained in our previous Note.
We state the connection between this theorem and the Peierls's barriers as defined by …

In this paper, M denotes a connected compact manifold without boundary, of dimension d,
and TM and T∗ M are its tangent and cotangent bundles. We shall consider the periodic …

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 …

In this paper, we focus on action-minimizing methods for contact Hamiltonian systems.
Based on implicit variational principles introduced in Wang et al.(Nonlinearity 30: 492–515 …

ARNOLD DIFFUSION IN HAMILTONIAN SYSTEMS: A PRIORI UNSTABLE CASE Chong-Qing
Cheng & Jun Yan Abstract 1. Introduction In this Page 1 j. differential geometry 82 (2009) …

Given a dynamical system and a function f from the state space to the real numbers, an
optimal orbit for f is an orbit over which the time average of f is maximal. In this paper we …