| Preface | p. xiii |
| Acknowledgements | p. xvii |
| Theory | |
| General introduction: chaos and economics | p. 3 |
| Introduction | p. 3 |
| An intuitive definition of chaos | p. 4 |
| The discovery of chaos | p. 6 |
| Chaotic dynamics and business cycles | p. 8 |
| Equilibrium and disequilibrium dynamics | p. 11 |
| The impact of chaos theory on economics | p. 15 |
| Chaos theory and statistical inference | p. 18 |
| A few caveats | p. 22 |
| The content of the book | p. 24 |
| Basic mathematical concepts | p. 27 |
| Vector fields, flows and maps | p. 27 |
| Conservative and dissipative systems | p. 32 |
| Invariant [small alpha]- and [small omega]-limit, attracting sets. Attractors | p. 37 |
| Basic types of attractors | p. 44 |
| Stability | p. 47 |
| Linearization | p. 48 |
| Lyapunov direct method | p. 54 |
| Dynamically equivalent systems. Conjugacy | p. 55 |
| Bifurcations | p. 59 |
| Hopf bifurcation for flows | p. 63 |
| Hopf bifurcation for maps (or Neimark bifurcation) | p. 67 |
| Ergodic theory of chaos | p. 70 |
| Probability space. Invariant measure | p. 70 |
| Ergodicity | p. 72 |
| Absolute continuity and observability | p. 73 |
| Some examples of invariant measures | p. 75 |
| Entropy and Lyapunov characteristic exponents | p. 77 |
| A user's guide | p. 81 |
| Surfaces of sections and Poincare maps | p. 87 |
| Introduction | p. 87 |
| 'Canonical' Poincare maps | p. 88 |
| Numerical Poincare maps | p. 94 |
| Spectral analysis | p. 101 |
| The Fourier transform | p. 101 |
| Power spectral density | p. 103 |
| Applications of spectral analysis | p. 104 |
| The estimate of PSD. Aliasing | p. 110 |
| Estimating PSD with finite samples | p. 111 |
| Lyapunov characteristic exponents | p. 115 |
| The theory of LCEs | p. 115 |
| Lyapunov characteristic exponents and chaos | p. 121 |
| Numerical computation of LCEs | p. 123 |
| Computation of LCEs from experimental data | p. 124 |
| Dimensions | p. 127 |
| Fractal dimension | p. 127 |
| Numerical computations | p. 133 |
| Other measures of fractal dimension | p. 135 |
| Symbolic dynamics | p. 139 |
| The space of symbol sequences. The shift map | p. 139 |
| The Smale horseshoe and the geometry of chaos | p. 143 |
| Transition to chaos. Theoretical predictive criteria | p. 149 |
| Introduction | p. 149 |
| Homoclinic orbits and horseshoes | p. 150 |
| Codimension one routes to chaos: one-dimensional maps | p. 153 |
| Period-doubling | p. 158 |
| Intermittency | p. 165 |
| Saddle connection, or 'blue sky catastrophe' | p. 169 |
| Quasi-periodic route to chaos | p. 173 |
| Analysis of experimental signals - some theoretical problems | p. 179 |
| The theoretical problem | p. 179 |
| The reconstruction of the attractor - some difficulties | p. 181 |
| Singular spectrum analysis | p. 183 |
| Filtering away noise | p. 186 |
| Applications to economics | |
| Discrete and continuous chaos | p. 193 |
| Introduction | p. 193 |
| Probability distributions of lags | p. 195 |
| A feedback representation of lags | p. 197 |
| Symptomatology of chaos | p. 201 |
| A reconstructed 1D map | p. 210 |
| Conclusions | p. 213 |
| Cycles and chaos in overlapping-generations models with production | p. 215 |
| The basic model | p. 215 |
| Constant relative risk aversion: forward dynamics | p. 218 |
| Constant absolute risk aversion: backward dynamics | p. 221 |
| Chaos in a continuous-time model of inventory business cycles | p. 241 |
| The model | p. 241 |
| Lag structure and complex behaviour | p. 244 |
| Parameter analysis and numerical simulations | p. 247 |
| A few complications and conclusions | p. 253 |
| Analysis of experimental signals - applications | p. 259 |
| Detecting deterministic chaos | p. 259 |
| Applications of SSA. Noiseless data | p. 264 |
| Reconstruction of attractors with noisy data | p. 268 |
| Application of the SSA analysis to financial data | p. 273 |
| Differentiated series | p. 273 |
| Detrended series | p. 278 |
| Conclusions | p. 279 |
| Software | |
| DMC Manual | p. 285 |
| Installation | p. 285 |
| MS-DOS | p. 285 |
| Macintosh | p. 287 |
| What to do if DMC does not work | p. 288 |
| Graphical user interface | p. 288 |
| The editor | p. 293 |
| Functions | p. 295 |
| MODEL | p. 295 |
| EVAL | p. 298 |
| PLOT | p. 303 |
| STAT | p. 307 |
| FILES | p. 313 |
| UTIL | p. 315 |
| OPTS | p. 317 |
| QUIT | p. 318 |
| Internal menu commands | p. 318 |
| DMC internal compiler | p. 321 |
| References | p. 329 |
| Index | p. 339 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
