Arnolʹd, V. I.

"In a time of protracted economic crisis, failing political systems, and impending environmental collapse, one strand in our collective cultural myth of Progress--the technological--remains vibrantly intact, surging into the future at ramming speed. Amid the seemingly exponential proliferation of machine intelligence and network connectivity, and the increasingly portentous implications of emerging nanotechnology, futurists and fabulists look to an imminent historical threshold whereupon the nature of human existence will be radically and irrevocably transformed. The Singularity, it is supposed, can be no more than a few years off; indeed, some believe it has already begun. Technological Singularity--a trope conceived in science fiction and subsequently adopted throughout technocultural discourse and beyond--is the primary site of interpenetration between technoscientific and science-fictional figurations of the future, a territory where longstanding binary oppositions between science and fiction, and between present and future, are rapidly dissolving. In this groundbreaking volume, the first to mount a sustained and wide-ranging critical treatment of Singularity as a subject for theory and cultural studies, Raulerson draws SF texts into a complex dialogue with contemporary digital culture, transhumanist movements, political and economic theory, consumer gadgetry, gaming, and related vectors of high-tech postmodernity. In theorizing Singularity as a metaphorical construct lending shape to a range of millennial anxieties and aspirations, Singularities also makes the case for a recent and little-understood subgeneric formation--postcyberpunk SF--as a cohesive body of work, engaged in a shared literary project that is simultaneously shaping, and shaped by, purportedly nonfictional technoscientific discourses"--Publisher.

Dynamical Systems IV Symplectic Geometry and its Applications by V.I.Arnol'd, B.A.Dubrovin, A.B.Givental', A.A.Kirillov, I.M.Krichever, and S.P.Novikov From the reviews of the first edition: "... In general the articles in this book 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.Society Newsletter 1991 "... Here, as well as elsewhere in this Encyclopaedia, 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 and, moreover, they are usually written by the experts in the field. ..." Medelingen van het Wiskundig genootshap 1992 !

Topological Methods in Hydrodynamics is the first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. The necessary preliminary notions both in hydrodynamics and pure mathematics are described with plenty of examples and figures. The book is accessible to graduate students as well as to pure and applied mathematicians working in the fields of hydrodynamics, Lie groups, dynamical systems, and differential geometry.

Translated from the Russian by E.J.F. Primrose "Remarkable little book." -SIAM REVIEW V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.

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.

"Mathematics: The New Golden Age offers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathematicians: Hilbert's tenth problem and the four-color theorem, Gaussian integers, chaotic dynamics and the Mandelbrot set, infinite numbers, and strange number systems. Why a "new golden age"? According to Keith Devlin, we are currently witnessing an astronomical amount of mathematical research. Charting the most significant developments that have taken place in mathematics since 1960, Devlin expertly describes these advances for the interested layperson and adroitly summarizes their significance as he leads the reader into the heart of the most interesting mathematical perplexities - from the biggest known prime number to the Shimura-Taniyama conjecture for Fermat's Last Theorem."--BOOK JACKET.