Dynamical Systems IV

1. Front Matter

   Pages i-vii

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2. Symplectic Geometry

   • V. I. Arnol’d, A. B. Givental’

   Pages 1-136

3. Geometric Quantization

   • A. A. Kirillov

   Pages 137-172

4. Integrable Systems. I

   • B. A. Dubrovin, I. M. Krichever, S. P. Novikov

   Pages 173-280

5. Back Matter

   Pages 281-286

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This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field.

• contact geometry
• dynamical systems
• manifold
• mathematical physics
• symplectic geometry

• Steklov Mathematical Institute, Moscow, USSR

  V. I. Arnol’d

• L.D. Landau Institute for Theoretical Physics, Academy of Sciences of the USSR, Moscow, USSR

  S. P. Novikov

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