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Dynamics, Statistics and Projective Geometry of Galois Fields (Hardcover, New): V. I. Arnol'd Dynamics, Statistics and Projective Geometry of Galois Fields (Hardcover, New)
V. I. Arnol'd
R1,131 R1,073 Discovery Miles 10 730 Save R58 (5%) Shipped within 7 - 12 working days

V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Mathematical Methods of Classical Mechanics (Hardcover, 2nd ed. 1989. Corr. 4th printing 1997): V. I. Arnol'd, K.... Mathematical Methods of Classical Mechanics (Hardcover, 2nd ed. 1989. Corr. 4th printing 1997)
V. I. Arnol'd, K. Vogtmann, A. Weinstein
R1,170 R1,002 Discovery Miles 10 020 Save R168 (14%) Shipped within 7 - 12 working days

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.

Singularities of Differentiable Maps - Volume II Monodromy and Asymptotic Integrals (Paperback, Softcover reprint of the... Singularities of Differentiable Maps - Volume II Monodromy and Asymptotic Integrals (Paperback, Softcover reprint of the original 1st ed. 1988)
V. I. Arnol'd, A.N. Varchenko, S.M. Gusein-Zade
R2,093 R1,630 Discovery Miles 16 300 Save R463 (22%) Shipped within 7 - 12 working days

The present. volume is the second volume of the book "Singularities of Differentiable Maps" by V.1. Arnold, A. N. Varchenko and S. M. Gusein-Zade. The first volume, subtitled "Classification of critical points, caustics and wave fronts," was published by Moscow, "Nauka," in 1982. It will be referred to in this text simply as "Volume 1." Whilst the first volume contained the zoology of differentiable maps, that is it was devoted to a description of what, where and how singularities could be encountered, this volume contains the elements of the anatomy and physiology of singularities of differentiable functions. This means that the questions considered in it are about the structure of singularities and how they function. Another distinctive feature of the present volume is that we take a hard look at questions for which it is important to work in the complex domain, where the first volume was devoted to themes for which, on the whole, it was not important which field (real or complex) we were considering. Such topics as, for example, decomposition of singularities, the connection between singularities and Lie algebras and the asymptotic behaviour of different integrals depending on parameters become clearer in the complex domain. The book consists of three parts. In the first part we consider the topological structure of isolated critical points of holomorphic functions. We describe the fundamental topological characteristics of such critical points: vanishing cycles, distinguished bases, intersection matrices, monodromy groups, the variation operator and their interconnections and method of calculation.

Singularities of Differentiable Maps - Volume I: The Classification of Critical Points Caustics and Wave Fronts (Paperback,... Singularities of Differentiable Maps - Volume I: The Classification of Critical Points Caustics and Wave Fronts (Paperback, Softcover reprint of the original 1st ed. 1985)
V. I. Arnol'd, A.N. Varchenko, S.M. Gusein-Zade
R1,996 Discovery Miles 19 960 Shipped within 7 - 11 working days

... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).

Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Hardcover, 1st ed 1988. 2nd printing 1994):... Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Hardcover, 1st ed 1988. 2nd printing 1994)
D.V. Anosov, S.K. Aranson, V. I. Arnol'd, I.U. Bronshtein, V.Z Grines, …
R2,873 R2,195 Discovery Miles 21 950 Save R678 (24%) Shipped within 7 - 12 working days

From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." "Journal de Physique"

Dynamical Systems VIII - Singularity Theory II. Applications (Hardcover, 1993 ed.): V. I. Arnol'd Dynamical Systems VIII - Singularity Theory II. Applications (Hardcover, 1993 ed.)
V. I. Arnol'd; Translated by J.S. Joel
R2,691 R2,134 Discovery Miles 21 340 Save R557 (21%) Shipped within 7 - 12 working days

This book is devoted to applications of singularity theory in mathematics and physics, covering a broad spectrum of topics and problems. "The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures." --ZENTRALBLATT MATH

Ecuaciones Diferenciales Ordinarias / Differential Ordinary Equations (Spanish, Paperback): V. I. Arnol'd Ecuaciones Diferenciales Ordinarias / Differential Ordinary Equations (Spanish, Paperback)
V. I. Arnol'd
R379 R356 Discovery Miles 3 560 Save R23 (6%) Out of stock
Dynamics, Statistics and Projective Geometry of Galois Fields (Paperback, New title): V. I. Arnol'd Dynamics, Statistics and Projective Geometry of Galois Fields (Paperback, New title)
V. I. Arnol'd
R637 Discovery Miles 6 370 Shipped within 7 - 11 working days

V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Lektsii Po Teorii Obyknovennyh Differentsial'nyh Uravnenij Chast' 2 (Russian, Paperback): V. I. Arnol'd Lektsii Po Teorii Obyknovennyh Differentsial'nyh Uravnenij Chast' 2 (Russian, Paperback)
V. I. Arnol'd
R611 Discovery Miles 6 110 Shipped within 7 - 11 working days

Eti lektsii chitalis' v dekabre 1968 goda - marte 1969 goda na vtorom kurse mehaniko-matematicheskogo fakul'teta MGU. Konspekt osnovan na zapisyah studentam A. Bogdanova, kotoromu avtor vyrazhaet svoyu blagodarnost'. V lektsiyah osveschayutsya takie temy, kak linejnye uravneniya s kompleksnym fazovym prostranstvom, klassifikatsiya osobyh tochek, ustojchivost' polozhenij ravnovesiya, kvazimnogochleny, linejnyj uravneniya s periodicheskimi koeffitsientami, variatsiya postoyannyh. This book, "Lektsii po teorii obyknovennyh differentsial'nyh uravnenij Chast' 2," by V.I. Arnol'd, is a replication of a book originally published before 1969. It has been restored by human beings, page by page, so that you may enjoy it in a form as close to the original as possible.

Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Paperback, Softcover reprint of the... Dynamical Systems I - Ordinary Differential Equations and Smooth Dynamical Systems (Paperback, Softcover reprint of the original 1st ed. 1988)
D.V. Anosov, S.K. Aranson, V. I. Arnol'd, I.U. Bronshtein, V.Z Grines, …
R2,120 Discovery Miles 21 200 Out of stock

From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." "Journal de Physique"

Dynamical Systems VIII - Singularity Theory II. Applications (Paperback, Softcover reprint of hardcover 1st ed. 1993): V. I.... Dynamical Systems VIII - Singularity Theory II. Applications (Paperback, Softcover reprint of hardcover 1st ed. 1993)
V. I. Arnol'd; Translated by J.S. Joel; Contributions by V. I. Arnol'd, V.V. Goryunov, O.V. Lyashko, …
R2,426 R2,301 Discovery Miles 23 010 Save R125 (5%) Out of stock

This book is devoted to applications of singularity theory in mathematics and physics, covering a broad spectrum of topics and problems. "The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures." --ZENTRALBLATT MATH

Dynamical Systems IV - Symplectic Geometry and its Applications (Paperback, Softcover reprint of hardcover 2nd ed. 2001): V. I.... Dynamical Systems IV - Symplectic Geometry and its Applications (Paperback, Softcover reprint of hardcover 2nd ed. 2001)
V. I. Arnol'd, S. P. Novikov; Translated by G. Wassermann, A. Dzhamay; Contributions by V. I. Arnol'd, …
R2,653 R2,514 Discovery Miles 25 140 Save R139 (5%) Out of stock

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 "

Dynamical Systems V - Bifurcation Theory and Catastrophe Theory (Paperback, Softcover reprint of the original 1st ed. 1994):... Dynamical Systems V - Bifurcation Theory and Catastrophe Theory (Paperback, Softcover reprint of the original 1st ed. 1994)
V.S. Afrajmovich, Yu.S. Il'yashenko, L.P. Shil'nikov; Edited by V. I. Arnol'd, N.D. Kazarinoff
R2,430 R2,305 Discovery Miles 23 050 Save R125 (5%) Out of stock

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

Singularities of Differentiable Maps, Volume 1 - Classification of Critical Points, Caustics and Wave Fronts (Paperback, 2012... Singularities of Differentiable Maps, Volume 1 - Classification of Critical Points, Caustics and Wave Fronts (Paperback, 2012 ed.)
V. I. Arnol'd, S.M. Gusein-Zade, A.N. Varchenko
R1,392 Discovery Miles 13 920 Out of stock

Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.

The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities."

Dynamical Systems V - Bifurcation Theory and Catastrophe Theory (Hardcover, 1994 ed.): V. I. Arnol'd Dynamical Systems V - Bifurcation Theory and Catastrophe Theory (Hardcover, 1994 ed.)
V. I. Arnol'd; Edited by V. I. Arnol'd; Translated by N. Kazarinoff; V.S. Afrajmovich, Yu.S. Il'yashenko, …
R2,480 R2,355 Discovery Miles 23 550 Save R125 (5%) Out of stock

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics," such as the characterization of personalities and the difference between a "genius" and a "maniac." Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.

Geometrical Methods in the Theory of Ordinary Differential Equations (Paperback, 2nd ed. 1988. Softcover reprint of the... Geometrical Methods in the Theory of Ordinary Differential Equations (Paperback, 2nd ed. 1988. Softcover reprint of the original 2nd ed. 1988)
V. I. Arnol'd; Edited by Mark Levi; Translated by J. Szucs
R1,902 Discovery Miles 19 020 Out of stock

Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.

Mathematical Methods of Classical Mechanics (Paperback, Softcover reprint of hardcover 2nd ed. 1989): V. I. Arnol'd Mathematical Methods of Classical Mechanics (Paperback, Softcover reprint of hardcover 2nd ed. 1989)
V. I. Arnol'd; Translated by K. Vogtmann, A. Weinstein
R1,167 Discovery Miles 11 670 Out of stock

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Catastrophe Theory (Paperback, 3rd, rev. and exp. ed. 1992. 2nd printing 2003): V. I. Arnol'd Catastrophe Theory (Paperback, 3rd, rev. and exp. ed. 1992. 2nd printing 2003)
V. I. Arnol'd; Translated by G.B. Wasserman, R.K. Thomas, Gerhard D. Wassermann
R963 Discovery Miles 9 630 Out of stock

The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.

Dynamical Systems, v. 6 - Singularity Theory 1 (Hardcover): V. I. Arnol'd Dynamical Systems, v. 6 - Singularity Theory 1 (Hardcover)
V. I. Arnol'd; Translated by Andrei Iacob
R1,971 Discovery Miles 19 710 Out of stock

The theory of singularities is an important part of various branches of mathematics: algebraic geometry, differential topology, geometric optics, etc. Here the focus is on the singularities of smooth maps and applications to dynamical systems - in particular, bifurcations. This includes the study of bifurcations of intersections of stable and unstable cycles. Along with the formal algebraic and analytic aspects of the theory, the authors consider global topological problems related to invariants. The authors have in mind a student reader, mathematician, or physicist, who wishes to learn the modern techniques of local mathematical analysis as an instrument for applied studies or a specialist in one of the applied areas who is looking for the necessary mathematical tools.

Geometrical Methods in the Theory of Ordinary Differential Equations (Hardcover, 2nd ed. 1988. 2nd printing 1996): V. I.... Geometrical Methods in the Theory of Ordinary Differential Equations (Hardcover, 2nd ed. 1988. 2nd printing 1996)
V. I. Arnol'd; Edited by Mark Levi; Translated by J. Szucs
R2,667 R2,528 Discovery Miles 25 280 Save R139 (5%) Out of stock

Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.

Singularities of Differentiable Maps, Volume 2 - Monodromy and Asymptotics of Integrals (Paperback, 2012 ed.): V. I.... Singularities of Differentiable Maps, Volume 2 - Monodromy and Asymptotics of Integrals (Paperback, 2012 ed.)
V. I. Arnol'd, S.M. Gusein-Zade, A.N. Varchenko
R1,504 Discovery Miles 15 040 Out of stock

The present volume is the second in a two-volume set entitled "Singularities of Differentiable Maps." While the first volume, subtitled "Classification of Critical Points" and originallypublishedas Volume82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of theanatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how they function."

Dynamical Systems VII - Integrable Systems Nonholonomic Dynamical Systems (Paperback, Softcover reprint of hardcover 1st ed.... Dynamical Systems VII - Integrable Systems Nonholonomic Dynamical Systems (Paperback, Softcover reprint of hardcover 1st ed. 1994)
V. I. Arnol'd, S. P. Novikov; Translated by A.G. Reyman, M.A. Semenov-Tian-Shansky; Contributions by A.T. Fomenko, …
R2,654 R2,515 Discovery Miles 25 150 Save R139 (5%) Out of stock

A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.

Singularity Theory I (Paperback, Softcover reprint of the original 1st ed. 1998): V. I. Arnol'd, V.V. Goryunov, O.V.... Singularity Theory I (Paperback, Softcover reprint of the original 1st ed. 1998)
V. I. Arnol'd, V.V. Goryunov, O.V. Lyashko, V.A. Vasil'ev; Translated by Andrei Iacob
R1,199 Discovery Miles 11 990 Out of stock

From the reviews: "... My general impression is of a particularly nice book, with a well-balanced bibliography, recommended!"Mededelingen van Het Wiskundig Genootschap, 1995"... The authors offer here an up to date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader, a carefully prepared and extensive bibliography ... makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. ... Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis."European Mathematical Society Newsletter, 1994

Dynamical Systems IV - Symplectic Geometry and its Applications (Hardcover, 2nd expanded and rev. ed. 2001): V. I.... Dynamical Systems IV - Symplectic Geometry and its Applications (Hardcover, 2nd expanded and rev. ed. 2001)
V. I. Arnol'd, B.A. Dubrovin, A.B. Givental, A.A. Kirillov, I.M. Krichever, …
R2,709 R2,570 Discovery Miles 25 700 Save R139 (5%) Out of stock

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 "

Dynamical Systems VII - Integrable Systems Nonholonomic Dynamical Systems (Hardcover, 1994 ed.): V. I. Arnol'd Dynamical Systems VII - Integrable Systems Nonholonomic Dynamical Systems (Hardcover, 1994 ed.)
V. I. Arnol'd; Contributions by A.T. Fomenko; Translated by A.G. Reyman; Edited by S. P. Novikov; Translated by M.A. Semenov-Tian-Shansky; Contributions by …
R2,710 R2,571 Discovery Miles 25 710 Save R139 (5%) Out of stock

A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.

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