Dynamical Systems Symplectic Geometry And Its Applications

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Dynamical Systems IV

V.I. Arnol'd,S.P. Novikov
Dynamical Systems IV Book PDF

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 43,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662067932

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Dynamical Systems IV by V.I. Arnol'd,S.P. Novikov Pdf

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.

Dynamical Systems IV

S.P. Novikov
Dynamical Systems IV Book PDF

Author : S.P. Novikov
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 44,8 Mb
Release : 2001-06-20
Category : Mathematics
ISBN : 3540626352

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Dynamical Systems IV by S.P. Novikov Pdf

From the reviews of the first edition:"... 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." Mededelingen van het Wiskundig genootshap 1992

Symplectic Geometry and Its Applications

Vladimir Igorevich Arnolʹd,Sergeĭ Petrovich Novikov
Symplectic Geometry and Its Applications Book PDF

Author : Vladimir Igorevich Arnolʹd,Sergeĭ Petrovich Novikov
Publisher : Springer
Page : 304 pages
File Size : 42,5 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39076000841481

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Symplectic Geometry and Its Applications by Vladimir Igorevich Arnolʹd,Sergeĭ Petrovich Novikov Pdf

Dynamical Systems IV

V.I. Arnol'd,S.P. Novikov
Dynamical Systems IV Book PDF

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer
Page : 0 pages
File Size : 40,5 Mb
Release : 2001-06-20
Category : Mathematics
ISBN : 3540626352

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Dynamical Systems IV by V.I. Arnol'd,S.P. Novikov Pdf

From the reviews of the first edition:"... 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." Mededelingen van het Wiskundig genootshap 1992

Structure of Dynamical Systems

J.M. Souriau
Structure of Dynamical Systems Book PDF

Author : J.M. Souriau
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202813

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Structure of Dynamical Systems by J.M. Souriau Pdf

The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.

An Introduction to Symplectic Geometry

Rolf Berndt
An Introduction to Symplectic Geometry Book PDF

Author : Rolf Berndt
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 51,9 Mb
Release : 2001
Category : Mathematics
ISBN : 0821820567

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An Introduction to Symplectic Geometry by Rolf Berndt Pdf

Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kähler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.

Dynamical System IV

Anonim
Dynamical System IV Book PDF

Author : Anonim
Publisher : Unknown
Page : 283 pages
File Size : 42,8 Mb
Release : 1990
Category : Geometric quantization
ISBN : 7506212609

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Dynamical System IV by Anonim Pdf

Dynamical Systems IV

Anonim
Dynamical Systems IV Book PDF

Author : Anonim
Publisher : Unknown
Page : 335 pages
File Size : 40,9 Mb
Release : 2001
Category : Celestial mechanics
ISBN : OCLC:47767721

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Dynamical Systems IV by Anonim Pdf

Nonlinear Dynamical Systems of Mathematical Physics

Denis L. Blackmore,Anatoli? Karolevich Prikarpatski?,Valeriy Hr Samoylenko
Nonlinear Dynamical Systems of Mathematical Physics Book PDF

Author : Denis L. Blackmore,Anatoli? Karolevich Prikarpatski?,Valeriy Hr Samoylenko
Publisher : World Scientific
Page : 563 pages
File Size : 47,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814327152

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Nonlinear Dynamical Systems of Mathematical Physics by Denis L. Blackmore,Anatoli? Karolevich Prikarpatski?,Valeriy Hr Samoylenko Pdf

This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field - including some innovations by the authors themselves - that have not appeared in any other book. The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville?Arnold and Mischenko?Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham?Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained. This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.