A conclusion to the trilogy that includes "The Map of Time" and "The Map of the Sky" finds its mysterious protagonist seeking an obscure magical book that will help him confess a dangerous secret to a lost loved one.

Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.

Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.

Developed and class-tested by a distinguished team of authors at two universities, this text is intended for courses in nonlinear dynamics in either mathematics or physics. The only prerequisites are calculus, differential equations, and linear algebra. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits -- short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed for use with any software package. And each chapter ends with a Challenge, guiding students through an advanced topic in the form of an extended exercise.

One CD-ROM disc in pocket.

Volume 2 of Directions in Chaos consists of the contributions made to the Beijing Summer School on Chaotic Phenomena in Nonlinear Systems held in August 1987.

BOOK OF ABSTRACTS CHAOS 2016 Chaotic Modeling and Simulation International Conference London, U.K., 23-26 May 2016

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.

Fallon Presley is different. She has a little something peculiar about her, but she embraces her oddness. Fallon never feels like she belongs with her family. She knows they love her, but she never fits in with the extended family. When her family suddenly dies in a car accident, she is left to sort through the family estate. With the help of her best friend, Bruce Andrews, they begin the task that opens up the mystery of who Fallon Presley is and where she came from. Fallon and Bruce step into a world of magic, witches, wolves, vampires, and the supernatural. Somewhere between the magic elements and the supernatural, Fallon finds herself, her true love, and maybe a little hidden magic.