(We would like to carry reviews of any of these books in future issues of UK Nonlinear News.)
Mass Market Paperback: 372 pages
Publisher: American Mathematical Society; ISBN: 0821828851; (July 1, 2002)
This book is a collection of survey articles on several topics related to the general notion of integrability. It stems from a workshop on "Mathematical Methods of Regular Dynamics" dedicated to Sophie Kowalevski. Leading experts introduce corresponding areas in depth. The book provides a broad overview of research, from the pioneering work of the nineteenth century to the developments of the 1970s through the present. The book begins with two historical papers by R. L. Cooke on Kowalevski's life and work. Following are 15 research surveys on integrability issues in differential and algebraic geometry, classical complex analysis, discrete mathematics, spinning tops, Painlevé equations, global analysis on manifolds, special functions, etc. It concludes with Kowalevski's famous paper published in Acta Mathematica in 1889, "Sur le problème de la rotation d'un corps solide autour d'un point fixe".
The book is suitable for graduate students in pure and applied mathematics, the general mathematical audience studying integrability, and research mathematicians interested in differential and algebraic geometry, analysis, and special functions.
This textbook provides an introduction to dynamic modelling in molecular cell biology, taking a computational and intuitive approach. Selected biological examples are used to motivate concepts and techniques used in computational cell biology through a progression of increasingly more complex cellular functions modelled with increasingly complex mathematical and computational techniques. Chapter summaries, detailed illustrations, examples and exercises are included throughout the text. Appendices containing mathematical and computational techniques are provided as a reference tool. Advanced undergraduate and graduate theoretical biologists, and mathematics students and researchers who wish to learn about modelling in cell biology, will find this book useful.
The core of this book was the beginning of a textbook written by Joel Keizer before his death in 1999. Joel founded and directed the Institute of Theoretical Dynamics a the University of California, Davis.
Series: Interdisciplinary Applied Mathematics, Vol. 20
448 pages hardcover
Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included.
Keywords: Dynamical systems, Small Divisors, Quasiperiodic ( orbits and flows). Mathematics Subject Classification (2000): 37C55, 37F25, 37F50, 37J40, 37K55, 47B39, 34L40
Contents: Hakan Eliasson: Perturbations of Linear Quasi-Periodic System.- Sergei B. Kuksin: KAM-Persistence of Finite-Gap Solutions.- Jean-Christophe Yoccoz: Analytic Linearization of Circle Diffeomorphisms.- Stefano Marmi and Jean-Christophe Yoccoz: Some Open Problems Related to Small Divisors.
2002. VIII, 198 p. Softcover
Recommended Retail Price: EUR 27,95
Series: Lecture Notes in Mathematics. VOL. 1784
This book provides modern investigation into the bifurcation phenomena of physical and structural problems. Systematic methods --based on asymptotic, stochastic, and group-theoretic standpoints-- are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes, etc.). Engineers may find this book, with its minimised mathematical formalism, to be a useful introduction to modern bifurcation theory. For mathematicians, static bifurcation theory for finite dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples.
Keywords: Bifurcation phenomena, Static bifurcation theory, Group-theoretic bifurcation theory, Bifurcation theory.
Contents: Introduction to Bifurcation Behaviour.- Critical Point and Local Behaviour.- Imperfection Sensitivity Laws.- Critical Initial Imperfections (I).- Stochasticity of Initial Imperfections (I).- Experimentally-observed Bifurcation Diagrams.- Group-theoretic Bifurcation Theory.- Bifurcation Behaviour of Dn-equivariant Systems.- Critical Initial Imperfections (II).- Stochasticity of Initial Imperfections (II).- Description of Bifurcation Behaviours.- Bifurcation of Cylindrical Sand Specimens.- Echelon-mode Formation.- Bifurcation of Steel Specimens.- Miscellaneous Aspects of Bifurcation Phenomena.- References.- Index.
2002. XVII, 411 p. 194 illus. Hardcover
Recommended Retail Price: EUR 74,95
Series: Applied Mathematical Sciences. Volume 149
This book grew out of the discussions and presentations that began during the Workshop on Emerging and Re-emerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed at ecologists, epidemiologists, immunologists, mathematicians, and scientists interested in the study of disease dynamics. The core of this first volume, Volume 125, covers tutorial and research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. The volume includes the study of cancer, HIV, pertussis, and tuberculosis. Beginning graduate students in applied mathematics, scientists in the natural, social, or health sciences or mathematicians who want to enter the fields of mathematical and theoretical epidemiology will find this book useful.
Series: The IMA Volumes in Mathematics and its Applications. Volume. 125
2002. Approx. 390 pp. Hardcover
This book grew out of the discussions and presentations that began during the Workshop on Emerging and Re-emerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed at ecologists, epidemiologists, immunologists, mathematicians, and scientists interested in the study of disease dynamics. The core of this second volume, Volume 126, covers research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. Contributions motivated by the study of diseases like influenza, HIV, tuberculosis, and macroparasitic like schistosomiasis are also included. This second volume requires additional mathematical sophistication, and graduate students in applied mathematics, scientists in the natural, social, and health sciences, or mathematicians who want to enter the field of mathematical and theoretical epidemiology will find it useful. The collection of contributors includes many who have been in the forefront of the development of the subject.
Series: The IMA Volumes in Mathematics and its Applications. Volume. 126
2002. Approx. 390 pp. Hardcover
First organised in 1981, the WASCOM conference to bring together researchers and scientists from all over the world to discuss problems, promote collaborations and shape future directions for research in the field of stability and wave propagation in continuous media.
This book constitutes the proceedings of the 11th edition of the conference, the first of the third millennium. The main topics are: