Introduction to discrete dynamical systems and chaos.

*(English)*Zbl 1127.37300
Wiley-Interscience Series in Discrete Mathematics and Optimization. New York, NY: Wiley (ISBN 0-471-31975-9/hbk). xiii, 328 p. (1999).

Publisher’s description: A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized.

This book makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks.

An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author’s 1993 book (see Zbl 0819.34001), but boasting at least 60% new, revised, and updated material, the present text is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.

This book makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks.

An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author’s 1993 book (see Zbl 0819.34001), but boasting at least 60% new, revised, and updated material, the present text is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.

##### MSC:

37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |

34-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

39-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to difference and functional equations |