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 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.

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: Poincaré recurrences, 12: Dynamical traps, 13: Fractal time, Kinetics, 14: General principles of kinetics, 15: Lévy processes and lévy 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

Graduate students, researchers and professionals working in physics, applied mathematics and engineering.

Professor George M. Zaslavsky Department of Physics and Courant Institute of Mathematical Sciences New York University