Review by Choice Review
This monograph is a major contribution to the dissemination of the new goemetrical (topological) ideas and methods that are deepening and, perhaps, revolutionizing our understanding of nonlinear dynamical systems not only in the biological, social, and economic sciences but also in the traditionally mathematically treated areas of mechanics, physics (including chemical physics), and engineering. Thompson has been a major contributor to these ideas and methods that originated a century ago in the pioneering work of Henri Poincar;e. That earlier work focused on Hamiltonian (conservative) systems, in particular those associated with celestial mechanics; the recent developments emphasize the study of dissapative systems. Furthermore, modern work has been able to successfully integrate efforts in theoretical, computational, and, surprisingly, experimental work. The present volume brings a richness to the subject matter only hinted at by the work of Ren;e Thom and the range of applications studied, primarily in the physical sciences, will make this book attractive to a wide audience. An important distinction emphasized throughout is that ``... between those catastrophic bifurcations at which there is a finite rapid dynamic jump to a new steady state, and subtle bifurcations in which the change in response manifests itself in the smooth growth of a new local attractor after the bifurcation point.'' In addition to being well written, the book is unusually well illustrated. Recommended unreservedly.-M. Levinson, University of Maine
Copyright American Library Association, used with permission.
Review by Choice Review
