Chaotic Dynamics of Nonlinear Systems

Description

Written when the young science of chaos was gaining a foothold in the scientific community, this book introduces the field's concepts, applications, theory, and technique. Suitable for advanced undergraduates and graduate students, researchers, and teachers of mathematics, physics, and engineering, the text's major prerequisite is familiarity with differential equations and linear vector spaces. Author S. Neil Rasband discusses the major models for the transitions to chaos exhibited by dynamic systems, introducing the "classical" topics and examples fundamental to the discipline. The most important routes to chaos are presented within a unified framework and supported by integrated problem sets. Topics include one- and two-dimensional maps, universality theory, fractal dimension, differential and conservative dynamics, and other subjects. The text is supplemented by a helpful glossary, references, and an index.

The book is intended to be a fairly self-contained exposition of the basic features of chaotic dynamics. The ten sections of the text follow almost a classical pattern, set by the numerous books that have already appeared on the subject during the last decade. The author discusses one- and two-dimensional maps, elements of universality theory, an introduction to differential and Hamiltonian dynamics, as well as different measures of chaos and their relation to fractals and complexity theory. Some sections require more serious mathematical background, but the vast majority of the material should be understandable to any student familiar with ordinary differential equations.
The presentation is lively and interesting without becoming imprecise, and the author succeeds well in skillfully mixing simple and more subtle concepts into an accessible, modern presentation.
In addition to one section specifically devoted to applications, each chapter is complemented with well-chosen exercises that are expected to be worked out and experimented upon by the reader. Some important topics like quantum chaos, noisy chaos, and symbolic dynamics are deliberately omitted. However, this should not affect the use of this textbook for its intended primary purpose, namely as a one-semester textbook for seniors or first-year graduate students.

Reviewed by V. Protopopescu