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Brief Summary


Part I. Investigation Methods of Complex and chaotic Nonlinear Dynamics.
Chap.1. Nonlinear Theory.
Chap.2. Delay model, SSA, and Brownian Motions.
Part II. Statistics of Complex and Chaotic Nonlinear Dynamics: Invariants and Rare Events.
Chap.3. Nonlinear Processes and Discrimination.
Chap.4. Statistical and Topological Invariants & Ergodicity.
Part III. Spectral & Time-frequency Theories and Waveforms: Regularity and Singularity.
Chap.5. Spectral & time-frequency analyses and Signal Processing.
Chap.6. The Atomic Decompositions of Signals.
Part IV. Economic Growth, Instability and Nonlinearity.
Chap.7. Evolution of Economic Growth Models.
Chap.8. Efficiency and Random Walk.
Appendix: Mathematics
A.1. Relations, Metric and Topological Structures.
A.2. Prehilbert, Hilbert and Banach Spaces.
A.4. Surfaces and Manifolds.
A.3. Complex number Fields, Holomorphic functions and Singularities.
A.5. Topology.
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A.6. Geometry axioms.
A.7. Series expansions.
A.8. Distribution theory.
A.9. Approximation theory.
A.10. Interpolation theory.
A.11. Numerical resolution of Equations.
A.12. Second-order differential equations.
A.13. Other reminders: Fourier series and transforms, etc.

Table of Contents

Table of Contents

List of Changes & Typos

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Revised on 06 Jun 2014.