Hamiltonian Chaos and Fractional Dynamics First Edition

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Written in a pedagogical style, richly illustrated, plenty of applications, examples, and problem sets. Presents some of the most complex and important features of Hamiltonian chaos. Comprehensive discussion of space-time fractality of chaotic dynamics. Includes detailed analysis of the foundations of statistical mechanics and Maxwell's demon. Includes unique material on non-KAM systems, symmetry of plane tilings, erasing of chaos, and cooling of particles. 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. Contents of the book : Chaotic Dynamics 1. Hamiltonian dynamics 2. Examples of Hamiltonian dynamics 3. Perturbed dynamics 4. Chaotic dynamics 5. Physical models of chaos 6. Separatrix chaos 7. Chaos and symmetry 8. Beyond the KAM-theory 9. Phase space of chaos Fractality of chaos 10. Fractals and chaos 11. Poincar?? recurrences 12. Dynamical traps 13. Fractal time Kinetics 14. General principles of kinetics 15. L??vy processes and l??vy flights 16. Fractional kinetic equation (FKE) 17. Renormalization group of kinetics (RGK) 18. Fractional kinetics equation solutions and modifications 19. Pseudochaos Applications 20. Complexity and entropy of dynamics 21. Complexity and entropy functions 22. Chaos and foundation of statistical mechanics 23. Chaotic advection (dynamics of tracers) 24. Advection by point vortices 25. Appendix 1 26. Appendix 2 27. Appendix 3 28. Appendix 4 29. Notes 30. Problems