(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach.
The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective.
The book is suitable for mathematicians and biologists interested in mathematical methods in biology
Proceedings of Symposia in Applied Mathematics, Volume 59.
Approximately 192 pages, hardcover
This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explore a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics.
The book will help readers who are not familiar with nonlinear dynamics to understand and enjoy sophesticated modern monographs on dynamical systems and chaos. Intended for courses in either mathematics, physics or engineering, prerequisites are calculus, differential equations and functional analysis.
AMS/IP Studies in Advanced Mathematics, Volume 28.
Approximately 288 pages, hardcover
The symmetries of a system of nonlinear ordinary or partial differential equations can be used to analyse, predict, and understand general mechanisms of pattern formation. This book applied symmetry methods to increasingly complex kinds of dynamic behaviour: equilibria, period-doubling, time-periodic states, homoclinic and heteroclinic orbits, and chaos. Examples are drawn from both ODEs and PDEs. In each case the type of dynamical behaviour being studied is motivated through applications, drawn from a wide variety of scientific disciplines ranging from theoretical physics to evolutionary biology. An extensive bibliography is provided.
Progress in Mathematics, Volume 200
334 pages, 182 illustrations, hardcover
This graduate textbook is a self-contained exposition of the well-posendess theory for nonlinear hyperbolic systems of conservation laws. The book is suitable for graduate students and researchers interested in nonlinear pdes and the mathematical aspecs of shock waves and propagating phase boundaries.
Approx 304 pp, softcover
This book provides a broad introduction to the subject of dynamical systems, suitable for a one- or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to such areas as number theory, data storage, and Internet search engines. This book grew out of lecture notes from the graduate dynamical systems course at the University of Maryland, College Park, and reflects not only the tastes of the authors, but also to some extent the collective opinion of the Dynamics Group at the University of Maryland, which includes experts in virtually every major area of dynamical systems.
252 pages 33 line diagrams 90 exercise, hardcover
Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence.
This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory.
Princeton Series in Applied Mathematics
Cloth | £29.95 | ISBN: 0-691-11298-3
Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.
2003 XVI, 419 p. Hardcover
Amazon.co.uk price: £56.45
This volume on applied dynamical systems provides the basic concepts for graduate students and researchers working in the area. It contains exercises and examples throughout. This new edition contains extensive material on normal forms, homoclinic orbits, symmetries, and Hamiltonian dynamics, making it a comprehensive book on dynamical systems from a geometrical and analytical point of view.
Texts in Applied Mathematics, Volume 2
2003/400 pages, 250 illustrations, hardcover.
This book is about normal forms - the simplest form into which a dynamical system can be put for the purpose of studying its behaviour in the neighborhood of a rest point - and about unfoldings, used to study the local bifurcations that the system can exhibit under perturbation. Ths book presents the advanced theory of normal forms, showing their interaction with representation theory, invariant theory, Groebner basis theory, and structure theory of rings and modules. In addition, this book includes algorithms suitable for use with computer algebra systems for computing normal forms. The interactions between the algebraic structure of normal forms and their geometrical consequences is emphasised.
Springer Monographs in Mathematics
2002/474 pages,15 illustrations, hardcover.
This book presents an introduction to the geometric theory of infinite dimensional dynamical systems. Many of the fundamental results are presented for asymptotically smooth dynamical systems that have applications to functional differential equations as well as clases of dissipative partial differential equations. However, as in the earlier edition, the major emphasis is on retarded functional differential equations. This updated version also contains much material on neutral functional differential equations. The results in the earlier edition on morse-Smale systems for maps are extended to a class of semiflows which include retarded functional differential equations and parabolic partial differential equations. In addition to being useful for researchers in the field, the book is appropriate for a graduate course in dynamical systems.
Applied Mathematical Sciences, Volume 47
]2002/296 pages, 15 illustrations, harcover.