Lyapunov functions : a weak KAM approach
type: Dataset
description: This thesis is divided into three parts. In the first part, we give a new description of chain-recurrence using an ultrametric barrier. This barrier allows to endow the space of chain-transitive components with an ultrametric structure, explaining its topology and leading to the famous result of Charles Conley about Lyapunov function decreasing along non chain-recurrent orbits. Most of the results, first given in the setting of a continuous map on a compact metric space are then generalised to multivalued map on arbitrary separable metric spaces. In the second part, we develop an Aubry-Mather theory for a homeomorphism on a compact metric space. In this setting, we introduce metric and topological Aubry set and Mañé set, allowing a better understanding of Lyapunov functions arising in such a dynamical system. In the last part, we prove a general density result for some counterexamples of Sard's theorem for which the set of critical points is a topological arc and we give applications to dynamics.
landing page: https://theses.hal.science/tel-00678325
identifier: NNT: 2011ENSL0654
keyword: chain-recurrence
keyword: dynamical-systems
keyword: fonctions-de-lyapunov
keyword: infoeu-reposemanticsdoctoralthesis
keyword: lyapunov-function
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: recurrence-par-chaines
keyword: sards-theorem
keyword: systemes-dynamiques
keyword: theoreme-de-sard
keyword: theorie-kam-faible
keyword: theses
keyword: weak-kam-theory
issued: 2026-05-25T01:50:48.188677
modified: 2026-05-25T01:50:48.188684
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Lyapunov functions : a weak KAM approach
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00678325
issued: 2026-05-25T01:50:48.302287
modified: 2026-05-25T01:50:48.151348