Symplectic Geometry of Integrable Hamiltonian Systems

Häftad, Engelska, 2003

Av Michèle Audin, Ana Cannas da Silva, Eugene Lerman, Ana Cannas Da Silva, M. Audin, A. Cannas de Silva

579 kr

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Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book).

Produktinformation

Utgivningsdatum2003-04-24
Mått170 x 244 x 14 mm
Vikt422 g
FormatHäftad
SpråkEngelska
SerieAdvanced Courses in Mathematics - CRM Barcelona
Antal sidor226
Upplaga2003
FörlagBirkhauser Verlag AG
ISBN9783764321673

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik
Matematisk fysik inom Naturvetenskap och teknik

A Lagrangian Submanifolds.- I Lagrangian and special Lagrangian immersions in C“.- II Lagrangian and special Lagrangian submanifolds in symplectic and Calabi-Yau manifolds.- B Symplectic Toric Manifolds.- I Symplectic Viewpoint.- II Algebraic Viewpoint.- C Geodesic Flows and Contact Toric Manifolds.- I From toric integrable geodesic flows to contact toric manifolds.- II Contact group actions and contact moment maps.- III Proof of Theorem I.38.- List of Contributors.

"This book, an expanded version of the lectures delivered by the authors at the 'Centre de Recerca Matemàtica' Barcelona in July 2001, is designed for a modern introduction to symplectic and contact geometry to graduate students. It can also be useful to research mathematicians interested in integrable systems. The text includes up-to-date references, and has three parts. The first part, by Michèle Audin, contains an introduction to Lagrangian and special Lagrangian submanifolds in symplectic and Calabi-Yau manifolds…. The second part, by Ana Cannas da Silva, provides an elementary introduction to toric manifolds (i.e. smooth toric varieties)…. In these first two parts, there are exercises designed to complement the exposition or extend the reader's understanding…. The last part, by Eugene Lerman, is devoted to the topological study of these manifolds."—ZENTRALBLATT MATH