(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
The book is a useful introduction to a survey of this field of active research. It is illustrated with many beautiful pictures of Julia sets, the Mandelbrot set, and other sets related to the theory. Mathematical Reviews
In the last fifteen years, the Mandelbrot set has emerged as one of the most recognisable objects in mathematics. While there is no question of its beauty, relatively few people appreciate the fact that the mathematics behind such images is equally beuatiful. This book presents lectures delivered on a wide range of topics during the AMS Short Course entitled "Complex Dynamical Systems: The Mathematics Behind the Mandlebrot and Julia Sets", held at the Joint Mathematics Meetings in Cincinnati in January 1994. Much of the book is accessible to anyone with a background in the basics of dynamical systems and complex analysis.
Proceedings of Symposia in Applied Mathematics,
1994; 209 pages; Hardcover;
Recently, there has been growing interest among engineers and applied mathematicians in the potential usefulness of chaotic behaviour. In this book, new mathematical ideas in nonlinear dynamics are described so that engineers can apply them in real physical systems, such as dry friction, chemical reactions, electronics, and cryptology. The monograph emphasizes mathematical precision by supplying fundamental definitions and theorems (but without proofs). Both continuous and discrete dynamical systems are considered.
1998 approximately 150pp softcover
Employing passivity as a common thread, this important monograph merges several streams of nonlinear control to find a constructive solution of the feedback stabilisation problem. It combines differential-geometric concepts with the analytic concepts of passivity, optimality, and Lyapunov stability, so that geometry may serve as a guide for construction of design procedures and analysis may provide robustness tools which geometry lacks. Also includes recursive designs and recursive Lyapunov designs for feedback, feedforward and interlaced structures. The book may be used for a first-year graduate course.
1997 313 pages hardcover
Communications and Control Engineering Series
This book presents a mathematically rigorous analysis of the nonlinear theory of shallow shells. It provides solutions to the general boundary value problems and gives both analytical and numerical methods for solving some of the problems in hand. Included are theorems of existence, results on the stability of solutions, justification of the numerical methods os solutions, and topological and variational approaches to the investigations. The new mathematical results allow for a deeper understanding of the mechanical contents of the equations of the theory and give a better idea of its possible applications. The first edition of the book, entitled Mathematical Problems In the Nonlinear Theory of Shallow Shells, was published in Russian in 1989. For this English edition the manuscript has been substantially revised and expanded.
1998, approximately 432 pp, hardcover
Applied Mathematical Sciences, Volume 133.
This monograph presents the fundamentals of global stabilisation and optimal control of nonlinear systems with uncertain models. It offers a unified view of deterministic disturbance attenuation, stochastic control, and adaptive control for nonlinear systems. The book addresses a large audience of researchers, students, engineers and mathematicians in the areas of robust and adaptive nonlinear control, nonlinear H-infinity stochastic nonlinear control (including risk-sensitive), and other related areas of control and dynamical systems theory.
1998 approximately 205pp hardcover
Communication and Control Engineering Series