(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
This book is a collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics (in the physiological and biological sciences) and statistics. It presents the proceedings of a four-day workshop entitled "Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences" held at the Centre de Recherches Mathématiques (CRM) in Montréal in July 1995. The goal of the workshop was to provide an exchange forum and to create a link between two diverse groups with a common interest in the analysis of nonlinear time series data.
The editors and peer reviewers of this work have attempted to minimise the problems of maintaining communication between the different scientific fields. The result is a collection of interrelated papers that highlight current areas of research in statistics that might have particular applicability to nonlinear dynamics and new methodology and open data analysis problems in nonlinear dynamics that might find their way into the toolkits and research interests of statisticians.
Features:
1997, 252 pages (hardcover)
ISBN 0-8218-0521-5
Fields Institute Communications, Volume 11.
This book systematically introduces the derivation of the two fundamental notions of "standard systems of differential equations" and "obstruction sets" and demonstrates their important properties and their applicability to stability problems. The Chinese edition of this book collected eight of Shantao's major articles on differentiable systems suring the period 1963-1984. In this English translation, two other appendices are added: " An extension of the C^{1} Closing Lemma" and "Obstruction Sets, Minimal Rambling Sets and Their Applications".
Liao Shantao is an outstanding mathematician in China. As a result of his profound and systematic research work, he won the Mathematics Prize in 1985 - awarded for the first time by the Third World Academy of Sciences - for his contributions to differentiable dynamical systems and other fields. He also won the National Natural Science Prize of China in 1987.
This series is published by Science Press New York and Science Press Beijing, and distributed worldwide, except in the People's Republic of China, Hong Kong, and Macao, by the American Mathematical Society.
Contents Certain ergodic properties of a differential system on a compact differentiable manifold; Standard systems of differential equations; Obstruction sets and strong transversality condition; Obstruction Sets (I); On the stability conjecture; Obstruction Sets (II); Standard systems of differential equations and obstruction sets with applications to structural stability problems; On characterisations of structural stability; Appendix to the Chinese edition; Appendix A. An extension of the C^{1} closing lemma; Appendix B. Obstruction sets, minimal rambling sets and their applications; Editor's postscripts.
May 1996, 383 pages (hardcover)
ISBN 1-880132-21-4
1991 Mathematics Subject Classification: 58
In order to tackle complex problems in the applied sciences, there is an increased demand for interdisciplinary research between mathematicians and researchers working in engineering, the sciences, and business. The mathematical sciences are undergoing rapid changes and the boundaries between them and other disciplines are blurring.
This volume contains survey articles and general thoughts and views on applied mathematics by the plenary speakers and panelists of a symposium on current and future directions in applied mathematics, which was held in the spring of 1996 at the University of Notre Dame.
Each speaker was asked to address specifically the open questions and important trends and available tools in their fields, what advice they would give to students entering these fields, and the links between pure and applied mathematics with respect to future developments.
Contributors Include:
A.M. Bloch | University of Michigan |
R. Brockett | Harvard University |
C.I. Byrnes | Washington University |
P.S. Constantin | University of Chicago |
N.M. Ercolani | University of Arizona |
R.E. Ewing | Texas A &M |
A. Friedman | IMA |
J. Gunawardena | BRIMS HP |
D.D. Holm | Los Alamos Natl Lab |
M.A. Khan | The Johns Hopkins University |
H.J. Landau | ATT |
A. Lindquist | Royal Institute of Technology |
B. Marcus | IBM Almaden |
J.E. Marsden | Caltech |
C.F. Martin | Texas Tech University |
G. Sanchez de Alvarez | Universidad Los Andes, Venezuela |
L.R. Taylor | University of Notre Dame |
1997-Spring 272pp 15 Illustrations
ISBN 0-8176-3956-X
Source: Mark Alber ( mark.s.alber.1@nd.edu).
For turbulent flows at relatively low speeds there exists an excellent mathematical model in the incompressible Navier-Stokes equations. Why then is the `problem of turbulence' so difficult? One reason is that these nonlinear partial differential equations appear to be insoluble, except through numerical simulations, which offer useful approximations, but little direct understanding.
Three recent developments offer new hope. First, the discovery by experimentalists of coherent structures in certain turbulent flows. Secondly, the suggestion that strange attractors and other ideas from finite dimensional dynamical systems theory might play a role in the analysis of the governing equations. And, finally, the introduction of the Karhunen-Loève or proper orthogonal decomposition. This book introduces these developments and describes how they may be combined to create low-dimensional models of turbulence, resolving only the coherent structures.
This book will interest engineers, especially in the aerospace, chemical, civil, environmental and geophysical areas, as well as physicists and applied mathematicians concerned with turbulence.
Cambridge Monographs on Mechanics
1996, 438pp (hardcover)
ISBN 55142-0
This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely interwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text.
The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
1996, 822pp (paperback)
ISBN 57557-5
Encyclopedia of Mathematics and its applications 54