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© 2001

Dynamical Systems IV

Symplectic Geometry and its Applications

  • V. I. Arnold
  • S. P. Novikov
Book

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 4)

Table of contents

  1. Front Matter
    Pages i-vii
  2. V. I. Arnol’d, A. B. Givental’, S. P. Novikov
    Pages 1-138
  3. A. A. Kirillov
    Pages 139-176
  4. B. A. Dubrovin, I. M. Krichever, S. P. Novikov
    Pages 177-332
  5. Back Matter
    Pages 333-335

About this book

Introduction

Dynamical Systems IV Symplectic Geometry and its Applications by V.I.Arnol'd, B.A.Dubrovin, A.B.Givental', A.A.Kirillov, I.M.Krichever, and S.P.Novikov From the reviews of the first edition: "... In general the articles in this book are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers." New Zealand Math.Society Newsletter 1991 "... Here, as well as elsewhere in this Encyclopaedia, a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction. As far as he could judge, most presentations seem fairly complete and, moreover, they are usually written by the experts in the field. ..." Medelingen van het Wiskundig genootshap 1992 !

Keywords

Hamiltonian systems Hamiltonsche Systeme Symplektische Geometrie geometric quantization geometrische Quantisierung inverse Streuungsmethode inverse scattering method symplectic geometry

Editors and affiliations

  • V. I. Arnold
    • 1
    • 2
  • S. P. Novikov
    • 3
    • 4
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.CEREMADEUniversité Paris 9 — DauphineParis Cedex 16-eFrance
  3. 3.Institute of Physical Sciences and TechnologyUniversity of MarylandCollege ParkUSA
  4. 4.L.D. Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRusssia

Bibliographic information

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Reviews

"... As is standard in volumes of the Encyclopaedia, all parts bring an excellent description of the chosen topics, with many examples, mostly without proofs. They can be found in the books and papers cited in a comprehensive bibliography."

European Mathematical Society Newsletter, p. 27, June 2003

From the reviews of the first edition:

"... In general the articles ... are well written in a style that enables one to grasp the ideas. The actual style is a readable mix of the important results, outlines of proofs and complete proofs when it does not take too long together with readable explanations of what is going on. Also very useful are the large lists of references which are important not only for their mathematical content but also because the references given also contain articles in the Soviet literature which may not be familiar or possibly accessible to readers." New Zealand Math. Soc. Newsletter 1991 "... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction. As far as he could judge, most presentations seem fairly complete..."

Mededelingen van het Wiskundig genootshap 1992