Weak Chaos and Quasi-Regular Patterns [Hardcover]

This is a paperback edition of the first title in the Cambridge Nonlinear Science Series.This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour.This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour.This book presents the fundamentals of chaos theory in conservative systems and provides a systematic study of the theory of transitional states of physical systems that lie between deterministic and chaotic behavior. The authors begin with the general concepts of Hamiltonian dynamics, stabililty, and chaos, and then discuss the theory of stochastic layers and webs and the numerous applications of this theory, particularly to pattern symmetry. Throughout, they are meticulous in providing a detailed presentation of the material, which enables the reader to learn the necessary computational methods and to apply them to other problems. The inclusion of computer graphics will aid understanding and the final section of the book contains a collection of patterns in art and living nature that will fascinate.Part I. General Concepts: Hamiltonian dynamics; Stability and chaos; Part II. Dymanic Order and Choas: The stochastic layer; Stochastic layer - stochastic sea transition; The stochastic web; Uniform web; Part III. Spatial Patterns: Two-dimensional patterns with quasi-symmetry; Two-dimensional hydrodynamic patterns with symmetry and quasi-symmetry; Chaos and streamlines; Part IV. Miscellanea: Patterns in art and nature; References; Index. The serious student of chaos will find this book well worth reading. As a technical review, it is presently lƒf