Nonlinear Dynamical Systems and Chaos (Progress in Nonlinear Differential Equations and Their Applications)

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This study of chaos, fractals and complex dynamics is intended for anyone familiar with computers. While keeping the mathematics to a simple level with few formulas, the reader is introduced to an area of current scientific research that was scarcely possible until the availability of computers. The book is divided into two main parts; the first provides the most interesting problems, each with a solution in a computer program format. Numerous exercises enable the reader to conduct his or her own experimental work. The second part provides sample programs for specific machine and operating systems; details refer to IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C. Other implementations of the graphics routines are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST.

Frontiers in Number Theory, Physics, and Geometry I: On Random Matrices, Zeta Functions and Dynamical Systems

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Frontiers in Number Theory, Physics, and Geometry I: On Random Matrices, Zeta Functions and Dynamical Systems
Pierre Emile Cartier
Manufacturer: Springer
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Binding: Hardcover

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Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization

ASIN: 3540231897

Book Description

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent.

More than ten years after a first meeting in 1989 between number theorists and physicists at the Centre de Physique des Houches, a second 2-week event focused on the broader interface of number theory, geometry, and physics.

This book is the result of that exciting meeting, and collects, in 2 volumes, extended versions of the lecture courses, followed by shorter texts on special topics, of eminent mathematicians and physicists.

The present volume has three parts: Random matrices, Zeta functions, Dynamical systems.

The companion volume is subtitled: On Conformal Field Theories, Discrete Groups and Renormalization and will be published in 2006 (Springer, 3-540-30307-3).

Dynamical Systems, Ergodic Theory and Applications (Encyclopaedia of Mathematical Sciences)

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Dynamical Systems, Ergodic Theory and Applications (Encyclopaedia of Mathematical Sciences)
L.A. Bunimovich , S.G. Dani , R.L. Dobrushin , M.V. Jakobson , I.P. Kornfeld , N.B. Maslova , Ya.B. Pesin , J. Smillie , Yu.M. Sukhov , and A.M. Vershik
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540663169

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This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. The ergodic theory of smooth dynamical systems is treated. Numerous examples are presented carefully along with the ideas underlying the most important results. Moreover, the book deals with the dynamical systems of statistical mechanics, and with various kinetic equations. For this second enlarged and revised edition, published as Mathematical Physics I, EMS 100, two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations were added. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.

Random Perturbations of Hamiltonian Systems (Memoirs of the American Mathematical Society)

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Random Perturbations of Hamiltonian Systems (Memoirs of the American Mathematical Society)
M. I. Freidlin , and A. D. Wentzell
Manufacturer: American Mathematical Society
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Binding: Paperback

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ASIN: 0821825860

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Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.

Adjoint Equations and Analysis of Complex Systems (Mathematics and Its Applications)

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Adjoint Equations and Analysis of Complex Systems (Mathematics and Its Applications)
Guri I. Marchuk
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792330137

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This is the first monograph to present the fundamentals of adjoint equation theory and perturbation algorithms, exemplifying their applications by solutions of complex problems of mathematical physics. The earlier Russian version (1992) has been completely revised and supplemented with many new results for this edition, thus offering a unique compilation of the author's research in many areas of applied mathematics over the years. The first part of the book describes the theory of adjoint equations and perturbation algorithms and gives examples of applications to problems. Nonlinear problems and statements of inverse problems based on methods of adjoint equations and perturbation are considered. The second part focuses on the applications of adjoint equations theory and perturbation algorithms to the solution of concrete problems, such as global and regional environmental protection, interaction between atmosphere and ocean, and data assimilation problems. This volume will be of great value to a wide range of researchers, workers and engineers interested in creating new technologies for designing and planning experiments, while solving concrete problems, especially for those working on numerical mathematics.

Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds: Classical and Quantum Aspects (Mathematics and Its Applications)

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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds: Classical and Quantum Aspects (Mathematics and Its Applications)
A.K. Prykarpatsky , and I.V. Mykytiuk
Manufacturer: Springer
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Binding: Hardcover

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This book is unique in providing a detailed exposition of modern Lie-algebraic theory of integrable nonlinear dynamic systems on manifolds and its applications to mathematical physics, classical mechanics and hydrodynamics. The authors have developed a canonical geometric approach based on differential geometric considerations and spectral theory, which offers solutions to many quantization procedure problems. Much of the material is devoted to treating integrable systems via the gradient-holonomic approach devised by the authors, which can be very effectively applied. Audience: This volume is recommended for graduate-level students, researchers and mathematical physicists whose work involves differential geometry, ordinary differential equations, manifolds and cell complexes, topological groups and Lie groups.

A Course in Mathematical Physics I and II: Classical Dynamical Systems and Classical Field Theory

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A Course in Mathematical Physics I and II: Classical Dynamical Systems and Classical Field Theory
W. Thirring
Manufacturer: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ProductGroup: Book
Binding: Paperback

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ASIN: 3540976094

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-- Kidder Smith, Bowdoin College, Philosophy East & West

Used in China as a book of divination and source of wisdom for more than three thousand years, the I Ching has been taken up by millions of English-language speakers in the nineteenth century. The first translation ever to appear in English that includes one of the major Chinese philosophical commentaries, the Columbia I Ching presents the classic book of changes for the world today.

Richard Lynn's introduction to this new translation explains the organization of The Classic of Changes through the history of its various parts, and describes how the text was and still is used as a manual of divination with both the stalk and coin methods. For the fortune-telling novice, he provides a chart of trigrams and hexagrams; an index of terms, names, and concepts; and a glossary and bibliography.

Lynn presents for the first time in English the fascinating commentary on the I Ching written by Wang Bi (226-249), who was the main interpreter of the work for some seven hundred years. Wang Bi interpreted the I Ching as a book of moral and political wisdom, arguing that the text should not be read literally, but rather as an expression of abstract ideas. Lynn places Wang Bi's commentary in historical context.

For beginners and devotees alike, Columbia's I Ching is the clearest and most authoritative translation of this ancient classic.

Customer Reviews:

One for the collection.......2003-09-14

The reviews on the Lynn book appear to break down to a partisanship between John Richard Lynn and Wilhelm. There's room in the library of the I Ching enthusiast for both. I happen to prefer Lynn, but refer frequently to Wilhelm. It's difficult to imagine either of the two absent from the shelf. I'm particularly grateful to Lynn for the comprehensive footnotes and historical notes to put each item in context.

Scholarship with insight.......2003-08-13

This is an outstanding blend of scholarship backed by a depth of research and expertise, melded with a sensitivity to what an oracle means to people, and how it is properly to be used. Lynn has recreated and organized the Wang Bi text of the I Ching (Wang Bi was a scholar and writer in ancient China who died at a tragically young age but accomplished extraordinary things on a truly Mozartean scale--his version of Lao Tzu's Tao Te Ching is still the most read and cited version of that work, and his insight into the I Ching, thanks to Prof. Lynn, deserves as much study). For those who are drawn to the ancient oracle as an insight guide rather than a parlor game or fortune-telling tool, Prof. Lynn's presentation of the Wang Bi I Ching is an essential first step. I would further recommend the work of Carol Anthony ("Guide to the I Ching") and her latest exploration of the I Ching from the perspective of helping one's inner learning to inform and enrich one's outer life, which has been written with Hanna Moog: it is called "I Ching: The Oracle of the Cosmic Way."

A different Confucian Yijing.......2000-12-14

What sets this apart from other translations of the Classic of Changes is that it is relatively recent work done on a relatively early collection of Changes-plus-commentaries. Indeed, Wang Bi's comments on the Changes, translated here, are the earliest known comments on the Changes, as Wang Bi lived just after the collapse of the Han dynasty.

The translator describes Wang Bi's approach as a blend of Confucianism, Legalism, and Daoism, although Daoism as we now know it had come into being barely 100 years prior, and the Changes has never been a particularly Daoist work to begin with, although it was finally admitted into the Daoist Canon centuries after its adoption by the Confucians. I would characterize Wang Bi's sensibility as predominantly Confucian. Indeed, Lynn acknowledges that Neo-Confucian interpretations of this classic would be much different had it not been for the legacy of Wang Bi.

This translation serves scholarship before all else, and is accordingly rife with footnotes, glosses, and annotations, which can make it rough to read. Nevertheless, this is one of the Five Classics, extremely important in the Confucian Canon, and Lynn has worked hard to bring us a complete translation of the Changes as read by Wang Bi. There is no doubt that it was a worthwhile effort.

For a neo-Confucian take on the Changes, the work of choice is still the Wilhelm-Baynes. For a pre-Confucian view, Whincup's translation is fascinating. By all means, avoid Ritsema and Karcher if what you desire is a translation of the Classic of Changes. As an introduction, I'd recommend the work at hand or Whincup's.

An exceptional translation.......1999-11-30

Richard John Lynn's translation of the I Ching has become one of my most precious books. He has found the style that brings back a very distant voice of ancient China: Wang Bi, a philosophical geenius who died at the age of 23 after having written the most outstanding commentaries ever of the I Ching and the Tao Te Ching. R.J.Lynn brings out the taoist touch of Wang Bi's philosophy by keeping the word "dao" in the English text. Some of his expressions are fun, like when someone's situation has come to a point of decline, Lynn translates Wang Bi with: "this one's dao has petered out". Somehow Lynn has brought Wang Bi's thought back to life.

Don't bother.......1999-02-23

This is a terrible book. The translation juxtaposes English words that are presumably equivalents of the original Chinese ideograms. The result is incomprehensible. The English words appear to flow in gramatically correct sentences but they make no sense. The translator appears to have no idea of what the I Ching is about or how it was used in Chinese culture. Unfortunately, I bought this book and wasted my money.

Classic of Changes, The: A New Translation of the I Ching As Interpreted by Wang Bi

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Classic of Changes, The: A New Translation of the I Ching As Interpreted by Wang Bi
Wang Bi
Manufacturer: Columbia Univ Pr
ProductGroup: Book
Binding: Hardcover
ASIN: B000KSFYFI

The Classic of Changes: A New Translation of the "I Ching" as Interpreted by Wang Bi

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The Classic of Changes: A New Translation of the "I Ching" as Interpreted by Wang Bi
Translator-Richard John Lynn
Manufacturer: Columbia University Press
ProductGroup: Book
Binding: Paperback
ASIN: B000OPQEJC

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CLASSIC OF CHANGES: A New Translation Of The I Ching As Interpreted by Wang Bi
Richard John (Tr.) Lynn
Manufacturer: Columbia University Press
ProductGroup: Book
Binding: Paperback
ASIN: B000OPQF2S

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