Concepts and results in chaotic dynamics. A short course. (English) Zbl 1107.37001
Theoretical and Mathematical Physics (Cham). Berlin: Springer (ISBN 3-540-34705-4/hbk). xii, 230 p. (2006).
The title of the book with additional word “ideas” would perfectly describe the content. More detailed description is given in Prefaces: “The book is not a mathematical treatise, but a course, which tries to combine two slightly contradicting aims: On one hand to present the main ideas in a simple way and to support them with many examples; on the other hand to be mathematically sufficiently precise, without undue detail.”
The book covers a good part of dynamical systems and concentrates mostly on hyperbolic behavior, ergodic properties and statistical mechanics as well as on experimental aspects. It would be not easy reading even for graduate students in mathematics and physics – the most obvious audience of this book. Especially some examples are quite laconic and most exercises are not trivial. On the other hand, there are a lot of good pictures and interesting comments. Concerning both the content and style, the book stays far away from the well-known book by the same authors [Iterated maps on the interval as dynamical systems. Progress in Physics, 1. Basel-Boston-Stuttgart: Birkhäuser (1980; Zbl 0458.58002)].
The book covers a good part of dynamical systems and concentrates mostly on hyperbolic behavior, ergodic properties and statistical mechanics as well as on experimental aspects. It would be not easy reading even for graduate students in mathematics and physics – the most obvious audience of this book. Especially some examples are quite laconic and most exercises are not trivial. On the other hand, there are a lot of good pictures and interesting comments. Concerning both the content and style, the book stays far away from the well-known book by the same authors [Iterated maps on the interval as dynamical systems. Progress in Physics, 1. Basel-Boston-Stuttgart: Birkhäuser (1980; Zbl 0458.58002)].
Reviewer: Jerzy Ombach (Kraków)
MSC:
| 37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |
| 37A25 | Ergodicity, mixing, rates of mixing |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
| 37A35 | Entropy and other invariants, isomorphism, classification in ergodic theory |
| 37D05 | Dynamical systems with hyperbolic orbits and sets |
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 82-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics |
