Discrete Weak KAM Theory
An Introduction through Examples and its Applications to Twist Maps
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
Provides a comprehensive and self-contained introduction to discrete weak KAM theory Offers an elementary approach to classical weak KAM and Aubry–Mather theory for Tonelli–Hamiltonian systems Contains new material on links between the discrete and the classical versions of weak KAM theory and explicit examples
Autor*in
Maxime Zavidovique
Themen in »Discrete Weak KAM Theory«
weak KAM theory Aubry Mather theory Hamiltonian systems optimization and optimal control theory symplectic twist maps of the annulus Ergodic Theory Partial Differential Equations