Table of contents

• Content
• Introduction
• To these notes

• Chapter I: One-dimensional variational problems
  • Regularity of the minimals
  • Examples
  • The accessoric variational problem
  • Extremal fields in the case n=1
  • The Hamiltonian description
  • Exercices for Chapter I
• Chapter II: Extremal fields and global minimals
  • Global extremal fields
  • An existence theorem
  • Properties of global minimals
  • Compactnes properties of global minimals
  • Irrational rotation numbers, Mather sets
  • Rational rotation numbers
  • Exercices for Chapter II
• Chapter III: Discrete systems, Applications
  • Monotone twist maps
  • A discrete variational problem
  • Three examples
  • The standard map
  • The Birkhoff billiard
  • The dual billiard
  • A second variational problem
  • Minimal geodesics on the torus
  • Hedlund's metric on the torus
  • Exercices for Chapter III

• Added literature (- April 2002)
• Literature
• Index