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Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor. Contents: Preface to the Second Edition Preface to the First Edition Introduction Symbolic Dynamics of Unimodal Maps Maps with Multiple Critical Points Symbolic Dynamics of Circle Maps Symbolic Dynamics of Two-Dimensional Maps Application to Ordinary Differential Equations Counting the Number of Periodic Orbits Symbolic Dynamics and Grammatical Complexity Symbolic Dynamics and Knot Theory Appendix References Index Readership: Researchers and students interested in chaotic dynamics. Keywords: Symbolic Dynamics;ChaosReview: Key Features: No previous knowledge of dynamical systems theory is required in order to read this book The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps
Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.
This volume is a collection of more than 7000 full titles of books and papers related to chaotic behaviour in nonlinear dynamics. Emphasis has been made on recent publications, but many publications which appeared before 1980 are also included. Many titles have been checked with the authors. The scope of the Bibliography is not restricted to physics and mathematics of chaos only. Applications of chaotic dynamics to other branches of natural and social sciences are also considered. Works related to chaotic dynamics, e.g., papers on turbulence dynamical systems theory and fractal geometry, are listed at the discretion of the author or the compiler. This Bibliography is expected to be an important reference book for libraries and individual researchers.
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.
The stories we tell in our attempt to make sense of the world—our myths and religion, literature and philosophy, science and art—are the comforting vehicles we use to transmit ideas of order. But beneath the quest for order lies the uneasy dread of fundamental disorder. True chaos is hard to imagine and even harder to represent. In this book, Martin Meisel considers the long effort to conjure, depict, and rationalize extreme disorder, with all the passion, excitement, and compromises the act provokes. Meisel builds a rough history from major social, psychological, and cosmological turning points in the imagining of chaos. He uses examples from literature, philosophy, painting, graphic art, science, linguistics, music, and film, particularly exploring the remarkable shift in the eighteenth and nineteenth centuries from conceiving of chaos as disruptive to celebrating its liberating and energizing potential. Discussions of Sophocles, Plato, Lucretius, Calderon, Milton, Haydn, Blake, Faraday, Chekhov, Faulkner, Wells, and Beckett, among others, are matched with incisive readings of art by Brueghel, Rubens, Goya, Turner, Dix, Dada, and the futurists. Meisel addresses the revolution in mapping energy and entropy and the manifold effect of thermodynamics. He then uses this chaotic frame to elaborate on purpose, mortality, meaning, and mind.
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.
This book focuses on explaining the fundamentals of the physics and mathematics of chaotic phenomena by studying examples from one-dimensional maps and simple differential equations. It is helpful for postgraduate students and researchers in mathematics, physics and other areas of science.
This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community. An interdisciplinary approach of interest to scientists and engineers working in a number of areas.