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.

Weak Chaos and Quasi-Regular Patterns (Cambridge Nonlinear Science Series, Series Number 1)

Science & Math

Zaslavskiî, Georgin Moiseevich

Usikov, D. A.

Chernikov, A. A.

Sagdeev, R.Z.

Physics

Cambridge University Press

Two sets of related computer software are also available. One, the student/teacher set, consists of six 51/4 inch IBM/XT/AT-compatible floppy diskettes on which eight scenarios of dynamic computer graphics are recorded. The second, the ATRS research diskette, contains the 'ATRS' program, which runs numerical experiments with mappings: constructing their phase portraits at any specified level of detail, studying their dynamics, correlation properties and the dependence of the dynamics of the processes on the initial condition and mapping coefficients. This unique book brings together the basic ideas of nonlinear theory essential for all branches of physics, including mechanics of continuous media, optics, radiophysics, solid state physics and plasma physics. The authors restrict the use of lengthy calculations to examples, and present the material in an informal style, based on qualitative analysis and physical estimates. Written by three pioneers in the field on nonlinear ph

Nonlinear Physics (CONTEMPORARY CONCEPTS IN PHYSICS)

Zaslavsky, George M.

Routledge

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Books by Usikov, D. A.