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Systèmes Intégrables Semi-Classiques: du Local au Global
San Vũ Ngọc, Université de Grenoble I, St Martin d'Heres, France
A publication of the Société Mathématique de France.
cover
Panoramas et Synthèses
2006; 156 pp; softcover
Number: 22
ISBN-10: 2-85629-221-6
ISBN-13: 978-2-85629-221-1
List Price: US$52
Member Price: US$41.60
Order Code: PASY/22
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This book presents a panorama of finite dimensional completely integrable Hamiltonian systems, in which classical aspects and quantum aspects will be living side by side, with similar appearances.

Classical mechanics is considered from the viewpoint of the geometric study of the singular Lagrangian foliation, whose regular leaves are the famous Liouville tori. Singularities are tackled using local and semi-global normal forms, which involve topological and symplectic invariants. Some relationships with toric varieties are explored.

Quantum integrable systems are treated in the framework of semiclassical microlocal analysis. Pseudo-differential calculus and Fourier integral operators offer efficient tools for discovering how the geometric features of these systems influence their spectral properties.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in discrete mathematics and combinatorics.

Table of Contents

  • Introduction
  • Introduction à l'analyse semi-classique
  • Exemples fondamentaux de systèmes intégrables
  • Théorie locale
  • Théorie semi-globale
  • Théorie globale
  • Bibliographie
  • Liste des figures
  • Index
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