Power Search
Low Price Guarantee
We Take School POs
Selected Chapters in the Calculus of Variations 2003 Edition
Contributor(s): Moser, Jürgen (Author)

View larger image

 ISBN: 3764321857     ISBN-13: 9783764321857
Publisher: Birkhauser
OUR PRICE: $52.24  

Binding Type: Paperback
Published: May 2003
Qty:

Annotation:

These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of J??rgen 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.

Click for more in this series: Lectures in Mathematics Eth Zurich
Additional Information
BISAC Categories:
- Mathematics | Calculus
- Mathematics | Geometry - Differential
- Mathematics | Linear & Nonlinear Programming
Dewey: 515.64
LCCN: 2003052194
Series: Lectures in Mathematics Eth Zurich
Physical Information: 0.39" H x 6.75" W x 9.37" L (0.60 lbs) 134 pages
Features: Bibliography, Illustrated, Index, Table of Contents
 
Descriptions, Reviews, Etc.
Publisher Description:
0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip- tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a related discrete variational problem and the corresponding minimal solutions. On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps. These maps appear in mechanics as Poincare maps. Such maps were studied by Birkhoff during the 1920s in several papers. In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets. His existence theorem is based again on a variational principle. Although these two investigations have different motivations, they are closely re- lated and have the same mathematical foundation. We will not follow those ap- proaches but will make a connection to classical results of Jacobi, Legendre, Weier- strass and others from the 19th century. Therefore in Chapter I, we will put together the results of the classical theory which are the most important for us. The notion of extremal fields will be most relevant. In Chapter II we will investigate variational problems on the 2-dimensional torus. We will look at the corresponding global minimals as well as at the relation be- tween minimals and extremal fields. In this way, we will be led to Mather sets.
 
Customer ReviewsSubmit your own review
 
To tell a friend about this book, you must Sign In First!