Hamiltonian Chaos and Fractional Dynamics

Paperback | November 9, 2008

byGeorge M. Zaslavsky

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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-ergodicand 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 thediscussed 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 ofdynamical 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.

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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-ergodicand non-well-mixing Hamiltonian dynamics. The ...

Professor George M. Zaslavsky Department of Physics and Courant Institute of Mathematical Sciences New York University
Format:PaperbackDimensions:336 pages, 9.21 × 6.14 × 0.9 inPublished:November 9, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199535485

ISBN - 13:9780199535484

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Table of Contents

Chaotic Dynamics1. Hamiltonian dynamics2. Examples of Hamiltonian dynamics3. Perturbed dynamics4. Chaotic dynamics5. Physical models of chaos6. Separatrix chaos7. Chaos and symmetry8. Beyond the KAM-theory9. Phase space of chaosFractality of chaos10. Fractals and chaos11. Poincare recurrences12. Dynamical traps13. Fractal timeKinetics14. General principles of kinetics15. Levy processes and levy flights16. Fractional kinetic equation (FKE)17. Renormalization group of kinetics (RGK)18. Fractional kinetics equation solutions and modifications19. PseudochaosApplications20. Complexity and entropy of dynamics21. Complexity and entropy functions22. Chaos and foundation of statistical mechanics23. Chaotic advection (dynamics of tracers)24. Advection by point vortices25. Appendix 126. Appendix 227. Appendix 328. Appendix 429. Notes30. Problems

Editorial Reviews

`Zaslavsky examines the new and realistic image of the origins of dynamic chaos and randomness by considering the Hamiltonian theory of chaos and such applications as the cooling of particles and signals, the control and erasing of chaos, polynomial complexity and Maxwell's Demon. 'SciTech Book News