Systemes intégrables semi-classiques - du local au global
The main aim of this book is to present a discussion of integrable systems, where both cases - classical systems and quantum systems - are treated together with their mutual relations. The book starts with a nice introduction containing interesting historical comments on classical and quantum integrable systems. The second chapter contains a review of the main properties of (various versions of) the theory of pseudo-differential operators, microlocal analysis and Fourier integral operators. Three representative examples of integrable systems (both on a classical and a quantum level) are treated in the next chapter. The main part of the book is divided into three parts first discussing local analysis of integrable systems (the main tool here being local normal forms), then (very important) semi-local analysis (including a discussion of numerical invariants) and finally treating its global aspects (with results on a globalization of Bohr-Sommerfeld conditions and the Duistermaat-Heckman formulae).