E-Book Overview
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.
E-Book Content
This book 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. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines. The authors begin with an introductory section covering Hamiltonian dynamics and the theory of chaos. Attention is then turned to the theory of stochastic layers and webs and to the applications of the theory. The connection between the various structural properties of the webs and the symmetry properties of patterns is investigated, including discussion of dynamic generators of patterns, hydrodynamic patterns and fluid webs. The final section of the book contains a fascinating collection of patterns in art and living nature. The authors have been meticulous in providing a detailed presentation of the material, e