(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
This book describes a revolutionary new approach to determining low-energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems and dynamical astronomy.
ISBN 0-691-09480-2.
Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Applications of these concepts underlie the algorithms used in computer graphics, mesh generation, and the evaluation of surface integrals. This Classics edition includes an updated bibliography and references to current software code.
Classics in Applied Mathematics 45
2003. xxvi+388 pages. Softcover.
ISBN 0-89871-544-X.
The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems, percolation and strange attractors. This new edition has been thoroughly revised throughout. The appendices of the original edition were taken out since more recent publications cover this material in more depth. Instead of the focused computer programs in BASIC, the authors provide 10 interactive JAVA-applets for this second edition.
2004, 866 pages, 125 illustrations, hardcover
ISBN 0-387-20229-3.
This second edition is a significant expansion over the first one which meanwhile has become a standard reference in complex system research and teaching. Probability concepts are more in-depth and the sections on Lévy laws and the mechanism for power laws have been greatly enlarged. Much material has been added to the chapter on renormalization group ideas. Further improvements can be found in the applications to earthquake and rupture models.
2004. 528 pages, 102 illustrations, hardcover.
ISBN 3-540-40754-5
Springer Series in Synergetics
This book explores the process of modelling complex systems in the widest sense of that term, drawing on examples from such diverse fields as ecology, epidemiology, sociology, seismology, as well as economics. It also provides the mathematical tools for studying the dynamics of these systems. Boccara takes a carefully inductive approach in defining what it means for a system to be "complex" (and at the same time addresses the equally elusive concept of emergent properties). This is the first text on the subject to draw comprehensive conclusions from such a wide range of analogous phenomena.
2004, 397 pages, 158 illustrations.
ISBN 0-387-40426-7
Graduate Texts in Contemporary Physics.