UK Nonlinear News, February 1999

WWW addresses for Publishers

Baltzer Science Publishers
Cambridge University Press
Walter de Gruyter
Oxford University Press
World Scientific

Publishers' Announcements

(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)

American Mathematical Society

Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julie Sets

Robert L. Devaney

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, Volume 49;
1994; 209 pages; Hardcover;
ISBN 0-8218-0290-9

New from Cambridge University Press

Dynamical Systems and Numerical Analysis

A.M. Stuart and A.R. Humphries

[Cambridge Monographs on Applied and Computational Mathematics 2]
published by Cambridge University Press

"Essential reading for all those interested in computational dynamical systems ... a very fine achievement" -- Proc. Edin. Math. Soc.

Dynamical systems are pervasive in the modelling of naturally occurring phenomena. Most of the models arising in practice cannot be completely solved by analytic techniques; thus, numerical simulations are of fundamental importance in gaining an understanding of dynamical systems. It is therefore crucial to understand the behaviour of numerical simulations of dynamical systems in order to interpret the data obtained from such simulations and to facilitate the design of algorithms which provide correct qualitative information without being unduly expensive.  These two concerns lead to the study of the convergence and stability properties of numerical methods for dynamical systems.

The first three chapters of this book contain the elements of the theoryof dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems, and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient, and Hamiltonian systems together with the convergence properties of equilibria, phase portraits, periodic solutions, and strange attractors under numerical approximation.

This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

1. Finite Dimensional Maps
2. Ordinary Differential Equations
3. Numerical Methods for Initial Value Problems
4. Numerical Methods as Dynamical Systems
5. Global Stability
6. Convergence of Invariant Sets
7. Global Properties and Attractors Under Discretization
8. Hamiltonian and Conservative Systems

700 pages 28 line diagrams 258 exercises
ISBN 0-521-64563-8 (Paperback)
Price UK pounds 24.95

For more information, consult the online catalogs at
and, or send enquiries to

New from Springer-Verlag

Chaos for Engineers

T. Kapitaniak

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
ISBN 3-540-63615-7

Constructive Nonlinear Control

R. Sepulchre, M. Jankovic, and P. Kokotovic

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
ISBN 3-540-76127-6
Communications and Control Engineering Series

Nonlinear Theory of Shallow Shells Dynamics

Iosif I. Vorovich

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
ISBN 0-387-98339-2
Applied Mathematical Sciences, Volume 133.

Stabilisation of Nonlinear Uncertain Systems

M. Krstic and H. Deng

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
ISBN 1-85233-020-1
Communication and Control Engineering Series

<< Move to UK Nonlinear News Issue 15 Index Page (February 1999).
Last Updated: 21st December 1998.