Discrete weak KAM theory : an introduction through examples and its applications to twist maps / Maxime Zavidovique.

Format:

Book

Author/Creator:

Zavidovique, Maxime, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2377.

Lecture notes in mathematics, 0075-8434 ; volume 2377

Language:

English

Subjects (All):

Mathematical optimization.

Calculus of variations.

Dynamics.

Differential equations.

Kolmogorov-Arnold-Moser theory.

Twist mappings (Mathematics).

Physical Description:

xv, 186 pages : color illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2025]

Summary:

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.

Contents:

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.

Notes:

Includes bibliographical references and index.

ISBN:

9783031968082

3031968085

OCLC:

1546648167

Publisher Number:

CIPO000300378