Rene Thom was the primary force behind the creation of Catastrophe Theory, and this is the book that brought his ideas forth. (This is actually the English translation of his original French edition.)Thom uses topology as his primary mathematical tool for describing and investigating catastrophes and stabilities. As such, this is primarily a qualitative, not a quantitative, approach. The advantage of this is that it allows Thom to spend a great deal of time discussing general characteristics without getting bogged down in formulae or proofs. Indeed, the book is largely text, interspersed with graphs and only the occasional polynomial or differential equations.
And Thom is very insightful when discussing those general characteristics. Along the way he comments on everything from embryology to societal structures as viewed from the perspective of catastrophe theory. Much of the value of the book is buried not in the technical results as it is in his understated comments and speculations regarding the myriad of applications he investigates. Alot of careful and deep thought is present, and there is a significant amount of pregnant wisdom inside.
I originally came to read Thom via the profound books of theoretical biologist Robert Rosen. As someone not conversant in topology or catastrophe theory, I can say that there were some parts that were a technical struggle, but the content is well worth the effort. Someone versed in the math of dynamical systems and topology would be the more typical target audience.
But I stress again that the technical value is equalled or surpassed by the insights Thom brings to understanding physical systems of many types.
Since there are no publishers notes here on Amazon, I will list the table of contents for you:
--------------------------------------------
Introduction
Form and Structural Stability
Structural Stability in Mathematics
Kinematic of Forms; Catastrophes
Elementary Catastrophes on R4 Associated with Conflicts of Regimes
General Morphology
The Dynamic of Forms
Biology and Topology
Local Models in Embryology
Global Models for a Living Being (Metazoa)
Models in Ultrastructure
The Basic Problems of Biology
From Animal to Man: Thought and Language
