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Selected chapters in the calculus of variations Jèurgen Moser ; lecture notes by Oliver Knill

By: Contributor(s): Series: Lectures in mathematics ETH ZèurichPublication details: Basel Boston Birkhèauser c2003Description: 132 pISBN:
  • 3764321857 (acid-free paper)
  • 0817621857 (Boston : acid-free paper)
Subject(s): DDC classification:
  • 515/.64
Other classification:
Contents:
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
Review: "These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jurgen 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 to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research."--BOOK JACKET
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Item type Current library Call number Status Date due Barcode
Carti IMAR II 34345 (Browse shelf(Opens below)) Available 0001365

Contine (bibliogr., index)

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

"These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jurgen 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 to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research."--BOOK JACKET

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