Transient chaos. Complex dynamics in finite-time scales
type: Item
instance of: scholarly article
title: Transient chaos. Complex dynamics in finite-time scales
zbMATH Open document ID: 1218.37005
DOI: 10.1007/978-1-4419-6987-3
author: Ying-Cheng Lai
author: T. Tél
published in: Applied Mathematical Sciences
publication date: 2010-09-14T00:00:00Z
review text: 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…
Mathematics Subject Classification ID: 37-02
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34H10
Mathematics Subject Classification ID: 81Q50
zbMATH DE Number: 5785275
zbMATH Keywords: transient chaos
zbMATH Keywords: crises
zbMATH Keywords: noise
zbMATH Keywords: fractal basin
zbMATH Keywords: chaotic scattering
zbMATH Keywords: chaotic advection
zbMATH Keywords: control and maintenance of chaos
zbMATH Keywords: time series analysis
Wikidata QID: Q99980039
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4419-6987-3
OpenAlex ID: W4237591246
description: scientific article