Bailin Hao – författare

A combinatorial method is developed in this book to explore the mysteries of chaos, which has became a topic of science since 1975. Using tools from theoretical computer science, formal languages and automata, the complexity of symbolic behaviors of dynamical systems is classified and analysed thoroughly. This book is mainly devoted to explanation of this method and apply it to one-dimensional dynamical systems, including the circle and interval maps, which are typical in exhibiting complex behavior through simple iterated calculations. The knowledge for reading it is self-contained in the book.

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.

This is a continuation of the previous two volumes of review papers on chaotic dynamics and related topics, published in 1987 and 1988 respectively. In addition to a few reviews written by active researchers specially for the volume, it also contains several reviews based on lectures delivered at the Spring School on Experimental Study of Chaotic Phenomena, held in Tianjing, China, in May 1989, and at the session on Nonlinear Dynamics during the Workshop on Condensed Matter, Molecular and Atomic Physics, held in June – August, 1989, at the International Centre for Theoretical Physics at Trieste, Italy. The emphasis has been made on multifractals, applied symbolic dynamics, the role of unstable orbits and transient chaos. This volume would be useful to graduate students and researchers in physical sciences and engineering.

This is an update of the Reprints and Introduction volume on Chaos first published in 1984. The general layout remains the same: an Introduction, followed by a collection of reprinted papers, and a Bibliography on chaos. The Introduction, while preserving its comprehensive yet elementary style, reflects recent developments in the field such as characterization of chaotic attractors by using experimental time series and the thermodynamic formalism of describing fractals. From the selected papers only less than one-third have been kept, the majority has been replaced by more recent research articles or reviews, including reviews on chaos in chemistry, biology, ecology and economy. In addition, the Bibliography has been extended to more than 2200 titles. On the whole, the volume is designed to be a source book for those entering the field of chaotic dynamics. The readership covers various branches of physical sciences and engineering. It may be used as a text book for graduate students as well.

This is an update of the Reprints and Introduction volume on Chaos first published in 1984. The general layout remains the same: an Introduction, followed by a collection of reprinted papers, and a Bibliography on chaos. The Introduction, while preserving its comprehensive yet elementary style, reflects recent developments in the field such as characterization of chaotic attractors by using experimental time series and the thermodynamic formalism of describing fractals. From the selected papers only less than one-third have been kept, the majority has been replaced by more recent research articles or reviews, including reviews on chaos in chemistry, biology, ecology and economy. In addition, the Bibliography has been extended to more than 2200 titles. On the whole, the volume is designed to be a source book for those entering the field of chaotic dynamics. The readership covers various branches of physical sciences and engineering. It may be used as a text book for graduate students as well.

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.

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.

Latest Edition: Applied Symbolic Dynamics and Chaos (2nd Edition)Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.