(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.
1999, 302pp, 56 figures.
This book is a continuation of the first volume - published in 1997 - and details the latest interesting developments. Mathematics has become more and more involved in the definition and use of fractal models, and the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Topics treated include locally self-similar processes, multifractal analysis, mathematical aspects, and applications in the physical sciences, chemical engineering, and image compression.
1999. Approximately 360pp.
Hardcover. ISBN 1-85233-163-1.
This book provides an up-to-date introduction to current research in fluctuations in spatially extended systems. The text begins with a general introduction to noise-induced phenomena in dynamical systems, followed by an extensive discussion of analytical and numerical tools needed to get information from stochastic partial differential equations. It then turns to particular problems described by stochastic partial differential equations, covering a wide part of the rich phenomenology of spatially extended systems, such as nonequilibrium phase transitions, domain growth, pattern formation, and front propagation.
Institute for Nonlinear Science.
1999. 320 pages. 120 illustrations.
Hardcover. ISBN 0-387-98855-6.
There has been a great deal of excitement over the last ten years concerning the emergence of new mathematical techniques for the analysis and control of nonlinear systems: witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos, and other complicated dynamical behaviour and the development of a comprehensive theory of nonlinear control. Coupled with this set of analytic advances has been the vast increase in computational power available both for the simulation of nonlinear systems as well as for the implementation in real time of sophisticated nonlinear control laws. This book lays out in a concise mathematical framework the tools and methods of analysis which underlie this diversity of applications.
1999/681pp, 193 illustrations. Hardcover.
Interdisciplinary Applied Mathematics, Volume 10.
This significantly enlarged and expanded second edition focuses on nonsmooth finite dimensional mechanical systems, subject to unilateral constraints. The following topics are discussed in detail and are illustrated with examples: short dynamics; multiple impacts; feedback control; Moreau's sweeping process; and complimentary formulations.
Communications and Control Engineering
1999. 552 pages. 84 illustrations.
Hardcover. ISBN 1-85233-143-7.
This textbook offers graduate students a rapid introduction to the language of ordinary differential equations. Mastery of the material in this book will provide a solid background for research in the subject of ordinary differential equations and applications of the theory to real world problems.
1999/584pp, 68 illustrations, Hardcover.