Synopses & Reviews
An introduction to certain aspects of developments in the modern theory of dynamics and simulation for a wide audience of scientifically literate readers. Unlike general texts on chaos theory and dynamical systems theory, this book follows the work on a specific problem at the very beginning of the modern era of dynamics, from its inception in 1954 through the early 1970s. It discusses such problems as the nonlinear oscillator simulation, the seminal discoveries at MIT in the early 1950s, the mathematical rediscovery of solitons in the late 1950s and the general problems of computability. In following these developments, the initial development of many of the now standard techniques of nonlinear modelling and numerical simulation are seen. No other text focuses so tightly and covers so completely one specific, pernicious problem at the heart of dynamics.
We hear a lot about dynamical systems theory these days-"chaos dy namics" is the popular idiom-but very little of this abstract discipline is taught in undergraduate or even in graduate school, unless that happens to be one's own field. People may have heard some of the terms, but they may not understand what a dynamicist does. Just what does a dynamicist do? Although I've been through the training, I spend much more time talk ing and thinking about dynamics than actually doing it, which is a circum stance that affords me an interesting perspective. Some time after defending my dissertation, when I stopped back by my alma mater on a visit through Boulder, I ran into one of my advisors, a practicing dynamicist, and he was excited to show me his new workstation and its resident software. Hope fully, by relating what I experienced then, I may in part help to answer my opening question. He sat down in front of a very large screen, at least 19 inches across, so closely, that it filled his field of view completely. At his fingertips were the usual mouse and keyboard. He fired up the software and chose a model; I think we were out to explore "just the standard map. " As the program began, the screen remained black, except for a small blinking cursor at the middle."
Table of Contents
Preface; Introduction; Part I: History; 1. The FPU Model and Simulation: "A Little Discovery"; 2. The FPU Research Program: Echoes on a String; 3. The Kolmogorov-Arnold-Moser Theorem: "Here Comes the Surprise"; 4. Research Threads Come Together: Harmonic Convergence; 5. Part II: Philosophy; 5. Steps to an Epistemology of Simulation; Appendix: Hamiltonian Dynamics: Language of Abstraction; Glossary; References; Index