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This paper argues that chaos theory provides a useful theorectical framework for understanding the dynamic evolution of… Expand Preface 1. Introduction 2. One-dimensional maps 3. Nonchaotic multidimensional flows 4. Dynamical systems theory 5. Lyapunov… Expand Over the past decade, there has been tremendous interest in studying the behavior of chaotic systems. They are characterized by… Expand Preface 1. Introduction Part I. Synchronization Without Formulae: 2. Basic notions: the self-sustained oscillator and its phase 3… Expand What is this business called 'chaos'? What does it deal with? Why do people think it's important? And how did the term 'chaos… Expand There are many striking similarities between the new science of chaos/complex-ity and second language acquisition (SLA) Chaos… Expand FRACTAL TIME SERIES. Failure of the Gaussian Hypothesis. A Fractal Market Hypothesis. FRACTAL (R/S) ANALYSIS. Measuring Memory… Expand Equilibrium Solutions, Stability, and Linearized Stability * Liapunov Functions * Invariant Manifolds: Linear and Nonlinear… Expand Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the… Expand We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series… Expand