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Discrete weak KAM theoryan introduction through examples and its applications to twist maps /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Discrete weak KAM theoryby Maxime Zavidovique.
Reminder of title:	an introduction through examples and its applications to twist maps /
Author:	Zavidovique, Maxime.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xv, 188 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Kolmogorov-Arnold-Moser theory.
Online resource:	https://doi.org/10.1007/978-3-031-96809-9
ISBN:	9783031968099$q(electronic bk.)

Discrete weak KAM theoryan introduction through examples and its applications to twist maps /
Zavidovique, Maxime.

Discrete weak KAM theoryan introduction through examples and its applications to twist maps /[electronic resource] :by Maxime Zavidovique. - Cham :Springer Nature Switzerland :2025. - xv, 188 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23771617-9692 ;. - Lecture notes in mathematics ;2035..

Chapter 1. Introduction. - Chapter 2. The discrete weak KAM setting -- Chapter 3. Characterizations of the Aubry sets -- Chapter 4. Mather measures, discounted semigroups -- Chapter 5. A family of examples -- Chapter 6. Twist maps.

The aim of this book is to present a self-contained account of discrete weak KAM theory. Putting aside its intrinsic elegance, this theory also provides a toy model for classical weak KAM theory, where many technical difficulties disappear, but where the central ideas and results persist. It therefore serves as a good introduction to (continuous) weak KAM theory. The first three chapters give a general exposition of the general abstract theory, concluding with a discussion of the relations between the results proved in the discrete setting and the analogous theorems of classical weak KAM theory. Several examples are studied and some key differences between the discrete and classical theory are highlighted. The final chapter is devoted to the historical problem of conservative twist maps of the annulus.

ISBN: 9783031968099$q(electronic bk.)

Standard No.: 10.1007/978-3-031-96809-9doiSubjects--Topical Terms:

968083
Kolmogorov-Arnold-Moser theory.

LC Class. No.: Q172.5.C45

Dewey Class. No.: 003.857

Discrete weak KAM theoryan introduction through examples and its applications to twist maps /
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520 $a The aim of this book is to present a self-contained account of discrete weak KAM theory. Putting aside its intrinsic elegance, this theory also provides a toy model for classical weak KAM theory, where many technical difficulties disappear, but where the central ideas and results persist. It therefore serves as a good introduction to (continuous) weak KAM theory. The first three chapters give a general exposition of the general abstract theory, concluding with a discussion of the relations between the results proved in the discrete setting and the analogous theorems of classical weak KAM theory. Several examples are studied and some key differences between the discrete and classical theory are highlighted. The final chapter is devoted to the historical problem of conservative twist maps of the annulus.
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