Chaos — The Interplay Between Stochastic and Deterministic Behaviour

1. Front Matter

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2. Stochastic processes from deterministic dynamics

   • Christian Beck

   Pages 1-19

3. The interplay of classical and quantum stochastics: Diffusion, measurement and filtering

   • V. P. Belavkin

   Pages 21-40

4. Event enhanced and piecewise deterministic quantum theory or the right jump at the right place

   • Ph. Blanchard, A. Jadczyk

   Pages 41-50

5. Wave mechanics: The interplay between stochastics and quanta

   • A.M. Cetto, L. de la Peña

   Pages 51-73

6. Lévy processes and relativistic quantum dynamics

   • Piotr Garbaczewski

   Pages 75-86

7. Quantum coherence and decoherence in a classically chaotic experimentally accessible quantum optical system

   • Robert Graham

   Pages 87-100

8. Anomalous diffusion, spontaneous localizations and the correspondence principle

   • Paolo Grigolini

   Pages 101-119

9. Quantum open systems as random classical dynamical systems

   • Z. Haba

   Pages 121-134

10. Large-Scale Structure of the Universe and Asymptotics of Burgers' Turbulence with Heavy-tailed Dependent Data Yiming Hue and

    • W. A. Woyczynskil, Yiming Hu

    Pages 135-149

11. Convergence of iterative methods in perturbation theory

    • H. R. Jauslini, M. Govin, M. Cibils

    Pages 151-159

12. Eigenfunction expansions for time dependent hamiltonians

    • H. R. Jauslin, S. Guerin, A. Deroussiaux

    Pages 161-168

13. Strange attractors in higher-dimensional phase space

    • Tomasz Kapitaniak, Jerzy Wojewoda

    Pages 169-177

14. Mathematical classification of complete chaos

    • Michael Keane

    Pages 179-182

15. Anomalous diffusion and Lévy statistics in intermittent chaotic systems

    • J. Klafter, G. Zumofen, M. F. Shlesinger

    Pages 183-210

16. Classical and quantum chaotic scattering

    • Ying-Cheng Lai

    Pages 211-234

17. From fractals to stochastic differential equations

    • Andrzej Lasota

    Pages 235-255

18. Dissipative structures and weak turbulence

    • Paul Manneville

    Pages 257-272

19. Entropy and quantum characteristic exponents. steps towards a quantum pesin theory

    • R. Vilela Mendes

    Pages 273-282

20. Rigorous numerics of chaotic dynamical systems

    • Marian Mrozek

    Pages 283-296

The study of chaotic behaviour of dynamical systems has triggered new efforts to reconcile deterministic and stochastic processes as well as classical and quantum physics. New efforts are made to understand complex and unpredictable behaviour. The papers collected in this volume give a broad overview of these activities. Readers will get a glimpse of the growing importance of Lévy processes for physics. They will find new views on fundamental concepts of quantum physics and will see many applications of chaotic and essentially random phenomena to a number of physical problems.

• Levy Stochastic processes
• Lévy process
• Stochastic processes
• classically chaotic dynamics
• dissipative dynamical systems
• quantization
• quantum fluctuations
• stochastic analysis
• stochastic process

"In my opinion this book is essential reading for anyone who wants to become or stay up to date in the modern developments of chaos and quantum chaology." Contemporary Physics

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