Transient chaos. Complex dynamics in finite-time scales
The purpose of this monograph is to introduce the reader to the exciting subject of transient chaos through a careful selection of results obtained over the last three decades. Being just temporal evolutions preceding the asymptotic dynamics, transients are important for the understanding of the evolution of many systems encountered in physics, biology, engineering, chemistry or social sciences. Various applications of transient chaos are listed at the very beginning in Table 1 with the references to chapters where they are dealt with. The material in the book is organized into the four parts which, in turn, are divided into chapters. In the first part, principal concepts, ideas, algorithms and theories required for understanding of transient chaos are discussed. The second part presents different physical manifestations of transient chaos. The topics addressed here include fractal basin boundaries, chaotic scattering, quantum chaotic scattering, and conductance fluctuations in nanostructures. Transient chaos in higher dimensions and spatially extended systems are discussed in Part III, where a highly nontrivial nature of the extension from one-dimensional case is emphasized. Applications of transient chaos to various physical, biological, chemical and engineering systems are considered in the final fourth part. In particular, chaotic advection in fluid flows, control and maintenance of transient chaos are covered along with the transient chaotic time-series analysis. Relevant auxiliary information on several technical issues (multifractal spectra, open random baker maps, semiclassical approximations and scattering cross sections) is collected in the appendices. The book has a plenty of illustrations, the most beautiful in full color. An exhaustive list of up-to-date references contains 858 items; the index in the end is well-organized and helpful. The authors did an excellent job providing both a theoretical background necessary for the understanding of the concept of transient chaos and related notions and an overview of a variety of transient-chaos related phenomena. This encyclopedic monograph, nicely written by two well-known experts in the field, will be of interest for graduate students, researchers and engineers who deal with dynamical systems and their applications and have a working knowledge of nonlinear dynamics and sustained chaos.
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