Selected chapters in the calculus of variations /

Selected chapters in the calculus of variations /

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These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jürgen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest. Students will find a rapid introduction...

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Bibliographic Details
Main Authors: Moser, Jürgen, 1928-, Moser, Jürgen, 1928-
Other Authors: Knill, Oliver
Format: Book
Language:English
Published: Basel ; Boston : Birkhäuser Verlag, c2003
Basel ; Boston : Birkhäuser, [2003], ©2003
Basel ; Boston : Birkhäuser, c2003
Basel ; Boston : ©2003
Basel ; Boston : c2003
Basel ; Boston, MA : c2003
Series:Lectures in mathematics ETH Zürich
Lectures in mathematics ETH Zürich
Lectures in mathematics ETH Zürich
Lectures in mathematics ETH Zürich
Subjects:
Calculus of variations
Global differential geometry
Mathematical optimization
Mathematics
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Table of Contents:
  • Introduction
  • 1. One-dimensional variational problems
  • 2. Extremal fields and global minimal
  • 3. Discrete Systems, applications
  • Bibliography
  • Remarks on the literature
  • Additional bibliography
  • 0.1 Introduction
  • 0.2. On these lecture notes
  • 1. One-dimensional variational problems
  • 1.1. Regulatory of the minimals
  • 1.2. Examples
  • 1.3. The accessory variational problem
  • 1.4. Extremal fields for n=1
  • 1.5. The Hamiltonian formulation
  • 1.6. Exercises to Chapter 1
  • 2. Extremal fields and global minimals
  • 2.1. Global extremal fields
  • 2.2. An existence theorem
  • 2.3. Properties of global minimals
  • 2.4. A priori estimates and a compactness property
  • 2.5. M[subscript [alpha]] for irrational [alpha], Mather sets
  • 2.6. M[subscript [alpha]] for rational [alpha]
  • 2.7. Exercises to chapter II
  • 3. Discrete Systems, Applications
  • 3.1. Monotone twist maps
  • 3.2. A discrete variational problem
  • 3.3. Three examples
  • 3.4. A second variational problem
  • 3.5. Minimal geodesics on T[superscript 2]
  • 3.6. Hedlund's metric on T[superscript 3]
  • 3.7. Exercises to chapter III
  • A. Remarks on the literature.
  • 0.1 Introduction
  • 0.2. On these lecture notes
  • 1. One-dimensional variational problems
  • 1.1. Regulatory of the minimals
  • 1.2. Examples
  • 1.3. The accessory variational problem
  • 1.4. Extremal fields for n=1
  • 1.5. The Hamiltonian formulation
  • 1.6. Exercises to Chapter 1
  • 2. Extremal fields and global minimals
  • 2.1. Global extremal fields
  • 2.2. An existence theorem
  • 2.3. Properties of global minimals
  • 2.4. A priori estimates and a compactness property
  • 2.5. M[subscript [alpha]] for irrational [alpha], Mather sets
  • 2.6. M[subscript [alpha]] for rational [alpha]
  • 2.7. Exercises to chapter II
  • 3. Discrete Systems, Applications
  • 3.1. Monotone twist maps.

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