This book is thematically divided into three parts. In the first part, the reader is slowly introduced to basic concepts of the theory of dynamical systems. Many simple linear and nonlinear examples are discussed. The second part is devoted to problems connected with stability, instability, and in particular, the concept of chaos. Again, a number of examples are presented, including the well-known Lorenz attractor and logistic map. The last part focuses on the dynamics of systems that are ‘complex’, which is seen as a special regime between stable and chaotic behaviour.

The book is written in an essentially non-technical language, which makes it easily accessible to an audience with only an elementary mathematical background. More importantly, the authors are obviously trying to discuss the problems with a very wide perspective and the book contains a lot of digressions into philosophical topics. The reader can thus also read (among others) about the anthropic principle, questions related to determinism and reductionism, and the philosophical background of doing mathematics in general. Despite the fact that some ideas could be considered to be a little speculative (as for example the suggestion that the review of the concept of “number” or “infinity” might lead to establishing a successful complexity theory), the book will certainly bring a lot of pleasure to readers with philosophical inclinations.

Reviewer:

dpr