Preface

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the field by some of the most important researchers in the area. The first contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the field. So we decided to transcribe it and include it here as the first section of the book. The dynamics of maps on the complex plane provide some of the most striking examples of chaos and fractal invariant sets in dynamics, and has been of great importance to the field because they are amenable to rigorous treatment. The first paper in the book is R. Devaney’s investigation of the dynamical properties of singularly-perturbed complex maps. He investigates Julia sets and other related sets which arise in maps with a pole, and classifies their dynamics. One of the most exciting developments in recent years is the application of dynamical systems techniques to complex networks of interacting components, each having their own internal dynamics, and each being coupled to other nodes. P. Ashwin, G. Orosz and J. Borresen review how complex dynamics can arise even in simple, fully symmetric and globally coupled networks. They make the important point that not only the network topology (which is usually emphasised in the literature), but also the properties of the coupling function are crucial to determine the system’s global dynamics. Fluid dynamics is an area that has always had a close relation with chaos. The motion of particles advected by time-dependent flows is a prime example of a chaotic system, and chaotic advection has been observed in many beautiful experiments. Most of the existing theoretical work considers advected particles as having