In the past few decades we have come to understand that even motions in simple systems can have complex and surprising properties. Chaotic Dynamics provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior in-depth scientific and mathematical knowledge. Richly illustrated throughout, examples are taken from classical mechanics whose elementary laws are familiar to the reader. In order to emphasize the general features of chaos, the most important relations are also given in simple mathematical forms, independent of any mechanical interpretation. A broad range of potential applications are presented, ranging from everyday phenomena through engineering and environmental problems to astronomical aspects. Chaos occurs in a variety of scientific disciplines, and proves to be the rule, not the exception. This book is primarily intended for undergraduate students in science, engineering, and mathematics.

• Clear pedagogical presentation, rich in illustrations, that provides a broad coverage of aspects of chaos • Presents important features of chaotic phenomena within a framework of classical mechanics • Includes many worked examples as well as problems with half of the solutions available to lecturers from solutions@cambridge.org

### Contents

Introduction; Part I. The Phenomenon: Complex Motion, Unusual Geometry: 1. Chaotic motions; 2. Fractal objects; Part II. Preparatory Concepts: 3. Regular motions; 4. Driven motions; Part III. Investigation of Chaotic Motion: 5. Chaos in dissipative systems; 6. Transient chaos in dissipative systems; 7. Chaos in conservative systems; 8. Chaotic scattering; 9. Applications of chaos; 10. Epilogue, outlook; Part IV. Miscellaneous: 11. Appendices; 12. Solutions to problems; 13. Bibliography.

### Reviews

'… a well-organised, beautifully illustrated volume covering the main points of chaotic dynamical systems, using intuitive mechanical examples to motivate clear and lucid discussions … It is certainly a book intended to teach or learn from … Throughout the work self-contained text capsules appear, expanding on issues raised in the discussions, and containing excellent summaries, histories, explanations and more potential applications … excellent layout and ordering … I would happily lend this book to any student wishing to begin learning the subject of chaotic dynamics, but I would certainly also demand its return.' Rob Sturman, University of Leeds

'… highly recommended as an introductory text …' Journal of Statistical Physics

'Even though there exists a lot of rather recent book on this subject, this manual is advisable for its clear presentation of the topics and for the simple and rigourous use of mathematical tools. A merit of this book is the cornerstone starting point: classical mechanics, which is the fundamental model for any other dynamical science. The book is planned mainly for undergraduate students of science, engineering and computational mathematics, but in the reviewer's opinion it could be useful to anybody interested in complex dynamics.' Zentralblatt MATH

'The book is excellent and I shall recommends it to my students'. Alistair Borthwick, Department of Engineering Science, University of Oxford

' … the book is thus very well suited to be an introductory text, and can also serve individual learning … It contains especially useful material also for completing a course on theoretical mechanics with regards to chaotic systems.' Dr Arnd Bäcker, Physik Journal

'…extremely engaging and very well suited for undergraduate students with basic training in classical mechanics… The innovative illustration scheme is one of the highlights of the book, particularly for establishing a clear correspondence between phase space behaviour and configuration space behaviour. In my opinion this is a book as no other for undergraduate chaos education.' Adilson E. Motter, Assistant Professor of Physics and Astronomy, Northwestern University