Hamiltonian Chaos and Fractional Dynamics

The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of the randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry and engineering.

Science & Math

Zaslavsky, George M.

Mathematics

Oxford University Press

The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics.The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry, and engineering.

Reference

Words, Language & Grammar

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)

Usikov, D. A.

Sagdeev, R.Z.

Physics

Routledge

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Books by Zaslavsky, George M.