ISBN-10:
0198526040
ISBN-13:
9780198526049
Pub. Date:
02/24/2005
Publisher:
Oxford University Press
Hamiltonian Chaos and Fractional Dynamics

Hamiltonian Chaos and Fractional Dynamics

by George M. ZaslavskyGeorge M. Zaslavsky
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Overview

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.

Product Details

ISBN-13: 9780198526049
Publisher: Oxford University Press
Publication date: 02/24/2005
Pages: 436
Product dimensions: 9.30(w) x 6.40(h) x 1.20(d)

About the Author

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

Table of Contents

Part 1 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. Weak chaos and symmetry
8. Beyond the KAM-theory
9. Phase space of chaos
Part 2 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, L vy flights, and Weierstrass random walks
16. Fractional kinetic equation (FKE)
17. Renormalization group of kinetics (RGK)
18. Fractional kinetics equation solutions and modifications
19. Pseudochaos
Part 4 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
Appendices
References
Index

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