Symplectic Geometry, Groupoids, and Integrable Systems: by Claude Albert, Pierre Dazord (auth.), Pierre Dazord, Alan

By Claude Albert, Pierre Dazord (auth.), Pierre Dazord, Alan Weinstein (eds.)

The papers, a few of that are in English, the remaining in French, during this quantity are according to lectures given throughout the assembly of the Seminare Sud Rhodanien de Geometrie (SSRG) prepared on the Mathematical Sciences learn Institute in 1989. The SSRG was once validated in 1982 by means of geometers and mathematical physicists with the purpose of constructing and coordinating learn in symplectic geometry and its purposes to research and mathematical physics. one of the topics mentioned on the assembly, a unique function used to be given to the idea of symplectic groupoids, the topic of fruitful collaboration concerning geometers from Berkeley, Lyon, and Montpellier.

Show description

Read Online or Download Symplectic Geometry, Groupoids, and Integrable Systems: Séminaire Sud Rhodanien de Géométrie à Berkeley (1989) PDF

Best nonfiction_8 books

Plate Stability by Boundary Element Method

1. 1 ancient historical past skinny plates and shells are universal structural parts in several civil, mechanical, aeronautical and marine engineering layout functions. flooring slabs, bridge decks, concrete pavements, sheet pile conserving partitions are all, below common lateral loading conditions, cases of plate bending in civil engineering.

Microwave Materials

Stable kingdom fabrics were gaining value lately particularly within the context of units that could offer invaluable infrastructure and suppleness for numerous human endeavours. during this context, microwave fabrics have a special position specially in quite a few gadget purposes in addition to in communique networks.

Molecular Magnetism: From Molecular Assemblies to the Devices

Molecular Magnetism: From Molecular Assemblies to the units stories the state-of-the-art within the region. it really is equipped in elements, the 1st of which introduces the elemental strategies, theories and actual concepts required for the research of the magnetic molecular fabrics, evaluating them with these utilized in the research of classical magnetic fabrics.

Controlled Release: A Quantitative Treatment

The concept that of managed unlock has attracted expanding cognizance over the past twenty years, with the purposes of this know-how proliferating in various fields in­ cluding medication, agriculture and biotechnology. learn and developmental efforts on the topic of managed liberate are multiplying in either and academia.

Additional info for Symplectic Geometry, Groupoids, and Integrable Systems: Séminaire Sud Rhodanien de Géométrie à Berkeley (1989)

Example text

Boyom G un groupe de Lie de symetrie de (lvI, w). On suppose que l'action symplectique de G dans (lvI, w) est reguliere et fermee. On fixe une suite (G k , Hk, Wk) ayant les proprietes requises. On a en particulier un diagramme analogue au diagramme (5). h, WI) et (M, w) sont reliees par la formule (6) Jr*WI - i*w = O. il1I ,wd est reguliere et fermee et dim MI = 2m. Le theoreme principal vaut donc pour (MI' WI)' Le theoreme de relevement assure que Ie theoreme principal vaut aussi pour (M,w). 0 6.

Les composantes connexes des Sx nj\;f1" (x, ,) E Mk xr sont des sous-varietes symplectiques de (I'vh. wd. Il resulte de l'egalite (6) que pour x E M k + l , les composantes connexes de M k + l n Sx sont des revetements symplectiques de (Mk+l' Wk+l). 2. 5. THEOREME DE RELEVEMENT ([12b]). Considerons les varietes sym- plectiques (Mk,Wk) et (Mk+I,Wk+l) reliees par Ie diagramme (5) et l'egaJite (6); on ales resultats qui suivent. (a) A toute structure bilagrangienne (AJk+I,Wk+I,F1,F2) all peut associer une autre structure bilagrangienne (A1 k, Wk,:tI ,:t2 ) qui verine les conditions 7r(:ti n Mk+d = F i , i = 1,2.

3) (AI,w) est graduee o 3. 1. Soit (M, w) une variete symplectique de dimension 2m. Soit F une sous-variete de dimension m de lvI, on notei: F '--+ AI Ie plongement inclusion. La sous-variete Fest appelee sous-variete lagrangienne si i*w = O. Soit F un feuilletage de dimension m dans AI. On dit que F est un feuilletage lagrangien de (AI, w) lorsque les feuilles de F sont des sousvarietes lagrangiennes de M. EXEMPLE: Soit X une variete de dimension m; l'espace total du fibre cotangent T* M muni de la 2-forme de Liouville Wo = do: possede un feuillet age lagrangien dont les feuilles sont les fibres de la fibration canonique 7r: T*X 1-+ X.

Download PDF sample

Rated 4.58 of 5 – based on 10 votes