Investigation Methods of Complex and Chaotic Nonlinear Dynamics -- Nonlinear Theory -- Delay Model, SSA and Brownian Motion -- Statistics of Complex and Chaotic Nonlinear Dynamics: Invariants and Rare Events -- Nonlinear Processes and Discrimination -- Statistical and Topological Invariants and Ergodicity -- Spectral and Time-Frequency Theories and Waveforms: Regularity and Singularity -- Spectral and Time–Frequency Analyses and Signal Processing -- The Atomic Decompositions of Signals -- Economic Growth, Instability and Nonlinearity -- Evolution of Economic Growth Models -- Efficiency and Random Walk.

Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body of knowledge regarding complex dynamics from various academic disciplines. Beyond its focus on economics and finance, including for instance the evolution of macroeconomic growth models towards nonlinear structures as well as signal processing applications to stock markets, fundamental parts of the book are devoted to the use of nonlinear dynamics in mathematics, statistics, signal theory and processing. Numerous examples and applications, almost 700 illustrations and numerical simulations based on the use of Matlab make the book an essential reference for researchers and students from many different disciplines who are interested in the nonlinear field. An appendix recapitulates the basic mathematical concepts required to use the book. .