Books in the Cambridge Nonlinear Science Series series

This 1998 book describes developments in understanding the formation of complex, disorderly patterns under conditions far from equilibrium. The application of fractal geometry and scaling concepts to the quantitative description and understanding is described. Discussion of self-similar fractals, multi-fractals and scaling methods facilitates applications in the physical sciences.

The book is written for students and scientists working in physics and related fields. It deals with thermodynamic methods used in nonlinear dynamics, a special branch of statistical physics. An easily readable introduction, the book can also be used as a textbook for special courses.

This book carries two important messages. First, it shows how an automaton universe with simple microscopic dynamics can exhibit macroscopic behaviour in accordance with the phenomenological laws of classical physics. Second, it demonstrates that lattice gases have spontaneous microscopic fluctuations which capture the essentials of actual fluctuations in real fluids.

This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models of nature. Common features of these apparently unrelated fields are emphasised and incorporated into a uniform mathematical description, including a large number of detailed examples and illustrations.

This book describes advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, and these are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium.

Fills a gap between the new fields of non-linear and chaotic dynamical systems, and the more traditional field of hydrodynamics and turbulence. The book contains the first coherent presentation of the applications of shell models to fully developed hydrodynamical turbulence.

This book brings together concepts from the important fields of semiconductor physics and nonlinear dynamics to examine transport phenomena in semiconductor systems. In doing so the wonders of nonlinearities, instabilities and chaos are revealed in a book that will be of great interest to semiconductor physicists and nonlinear scientists alike.

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour.

This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.

First recognized in 1665 by Christiaan Huygens, synchronization phenomena are abundant in science, nature, engineering and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae, and is based on qualitative intuitive ideas. The main effects are illustrated with experimental examples and figures, and the historical development is outlined. The remainder of the book presents the main effects of synchronization in a rigorous and systematic manner, describing classical results on synchronization of periodic oscillators, and recent developments in chaotic systems, large ensembles, and oscillatory media. This comprehensive book will be of interest to a broad audience, from graduate students to specialist researchers in physics, applied mathematics, engineering and natural sciences.

Almost all the many past studies on chaos have been concerned with classical systems. This book, however, is one of the first to deal with quantum chaos, the natural progression from such classical systems. This book will be of value to researchers and graduate students in physics and mathematics studying chaos, non-linear dynamics, quantum mechanics and solid-state science.