Dynamical Systems IV

"... 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

• Part I. Symplectic Geometry by V.I.Arnol'd, A.B.Givental'.-Part II. Geometric Quantization by A.A.Kirillov.-Part III. Integrable Systems I by B.A.Dubrovin, I.M.Krichever, S.P.Novikov.-Appendix A. Algebraic-Geometrical Integration of (2+1)-Systems.-Appendix B. Two-Dimensional Schrödinger Operators and Integrable Systems.-Appendix C. Integrability of Systems of Hydrodynamic Type. The Non-Linear WKB Method.-Appendix D. Spectral Theory of Two-Dimensional Periodic Operators. Historical Remarks Concerning Algebraic Geometry, Hamiltonian Systems and Spectral Theory.-References.