An Introduction to Chaos
Classical Examples by Way of Introduction
Historical Context
Feigenbaum’s Bifurcation
The Logistic Map
The Lorenz System
The Mathematical Theory of Chaos
Definitions and Notations
Topological and Metrical Spaces
Compactness and Completeness
Continuity
Discrete Dynamical Systems
Devaney’s Formulation of Chaos
Periodicity, Stability, and Regularity
Simplification of Discrete Dynamical Systems
Stability, Sensitivity, and Expansiveness
Chaos as Defined by Devaney (1989)
Examples of Chaotic Systems
Topological and Metrical Conjugacies
Other Formulations of Chaos
The Lyapunov Exponent
Topological and Metrical Entropy
From Theory to Practice
A Fundamental Tool: the Chaotic Iterations
Introducing the Chaotic Iterations
Chaotic Iterations as Devaney’s Chaos
Topological Properties of Chaotic Iterations
Characterization
The Lyapunov Exponent
Theoretical Proofs of Chaotic Machines
Chaotic Turing Machines
Practical Issues
Applications of Chaos in the Computer Science Field
Information Security
Steganography and Digital Watermarking
Pseudorandom Number Generators
Hash Functions
Wireless Sensor Networks
Video Surveillance
Secure Aggregation
Conclusion
Conclusion
Synthesis
Perspectives
Bibliography
Index