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The famous KAM theorem due to Kolmogorov, Arnold and Moser has proved critical in the theory of dynamical systems. A large and influential theory has built up around this result and there are applications in various branches of mathematics, chaos theory and physics. Arising from a lecture course given by the author at ENS Lyon, this book is ideal for graduate students. It contains a great deal of background and motivational material to help students come to grips with this important topic. However, the appeal of the book will extent to researchers will find this to be a useful resource, not least because Fathi has included numerous references that point to further, more advanced reading.
Table of Contents
1. Convex functions: Legendre and Fenchel; 2. Calculus of variations; 3. Calculus of variations for a Lagrangian convex in the fibres: Tonelli's theory; 4. The weak KAM theorem; 5. Conjugate weak KAM solutions; 6. A closer look at the Lax-Oleinik semi-group.