Dynamical Systems IV
Springer Berlin (Verlag)
978-3-540-62635-0 (ISBN)
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.
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.
"... 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
| Erscheint lt. Verlag | 20.6.2001 |
|---|---|
| Reihe/Serie | Encyclopaedia of Mathematical Sciences |
| Co-Autor | V.I. Arnol'd, B.A. Dubrovin, A.B. Givental', A.A. Kirillov, I.M. Krichever, S.P. Novikov |
| Übersetzer | G. Wassermann, A. Dzhamay |
| Zusatzinfo | XII, 336 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 612 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Dynamisches System • Dynamische Systeme • geometric quantization • Geometrische Quantisierung • Hamiltonian systems • Hamiltonsche Systeme • inverse scattering method • inverse Streuungsmethode • Symplectic Geometry • Symplektische Geometrie |
| ISBN-10 | 3-540-62635-2 / 3540626352 |
| ISBN-13 | 978-3-540-62635-0 / 9783540626350 |
| Zustand | Neuware |
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