Chaos, Noise and Fractals

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E. Roy Pike, L .A. Lugiato
CRC Press, Jan 1, 1987 - Science - 250 pages
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The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.
 

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Contents

Singular System Analysis with Application to Dynamical Systems
15
A Review of Progress in the Kicked Rotator Problem
28
Fractals in Quantum Mechanics?
47
Cantori and Quantum Mechanics
76
Chaos in the Micromaser
102
Chaos in a Driven Quantum Spin System
117
Fixed Points and Chaotic Dynamics of an Infinite Dimensional Map
137
The Arithmetic of Chaos
187
Limitations of the Rabi Model for Rydberg Transitions
200
Quasiprobability Distributions in Astable Dissipative Quantum Systems
222
Index
247
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