Symplectic Geometry and Analytical Mechanics

1. Front Matter

   Pages i-xvi

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2. Symplectic vector spaces and symplectic vector bundles

   • Paulette Libermann, Charles-Michel Marle

   Pages 1-52

3. Semi-basic and vertical differential forms in mechanics

   • Paulette Libermann, Charles-Michel Marle

   Pages 53-88

4. Symplectic manifolds and Poisson manifolds

   • Paulette Libermann, Charles-Michel Marle

   Pages 89-184

5. Action of a Lie group on a symplectic manifold

   • Paulette Libermann, Charles-Michel Marle

   Pages 185-274

6. Contact manifolds

   • Paulette Libermann, Charles-Michel Marle

   Pages 275-340

7. Back Matter

   Pages 341-526

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Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' Brown 'The point of a Pin'. in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thouglit to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sci­ ences has changed drastically in recent years: measure theory is used (non-trivially) in re­ gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homo­ topy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

• Host
• Lemma
• Vector field
• boundary element method
• calculus
• class
• constant
• electrical engineering
• equation
• foliation
• graphs
• integral
• lie group
• measure
• programming

` .. although orginally written in French, the translation by B.E. Schwartzbach is very good and the exposition thorough and careful. This book is a welcome addition to the literature. It will surely prove useful as a reference... '
Bulletin of the American Mathematical Society, Vol.20 No. 1, Jan.1989

• Université de Paris VII, Paris, France

  Paulette Libermann

• Université Pierre et Marie Curie (Paris VI), Paris, France

  Charles-Michel Marle