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 …

This article surveys results and conjectures in dynamical systems and other areas that
describe properties of 'almost every'function in some space, using a probabilistic (or …

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 …

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 …

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) …

We prove a form of Arnold diffusion in the a-priori stable case. Let H 0 (p)+ ϵ H 1 (θ, p, t), θ∈
T n, p∈ B n, t∈ T= R/T, be a nearly integrable system of arbitrary degrees of freedom n⩾ 2 …

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 …

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters
associated with positive definite Lagrangian systems for both the time-periodic case and the …