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＜電子ブック＞
Symplectic Geometry of Integrable Hamiltonian Systems / by Michèle Audin, Ana Cannas da Silva, Eugene Lerman
(Advanced Courses in Mathematics - CRM Barcelona. ISSN:22970312)

版	1st ed. 2003.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2003
大きさ	X, 226 p : online resource
著者標目	*Audin, Michèle author Cannas da Silva, Ana author Lerman, Eugene author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Manifolds (Mathematics) LCSH:Mathematical physics FREE:Differential Geometry FREE:Manifolds and Cell Complexes FREE:Mathematical Methods in Physics
一般注記	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 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) HTTP:URL=https://doi.org/10.1007/978-3-0348-8071-8

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