| Preface | p. ix |
| Acknowledgements | p. xii |
| Dynamical systems - general | p. 1 |
| Introduction to Part I | p. 3 |
| Astrophysical examples | p. 8 |
| Stellar population dynamics | p. 8 |
| One-zone model of a nonlinear stellar pulsator | p. 12 |
| Stellar orbits in a model galactic potential | p. 21 |
| One-element model of thermal convection | p. 28 |
| Patterns in a thermally unstable medium | p. 32 |
| Mathematical properties of dynamical systems | p. 40 |
| Local geometrical properties | p. 42 |
| Global attributes of dynamical systems | p. 71 |
| Elements of bifurcation theory | p. 83 |
| Dynamical systems near marginality | p. 93 |
| Fractal sets and dimensions | p. 102 |
| Properties of chaotic dynamics | p. 112 |
| Strange attractors | p. 113 |
| Sensitivity to initial conditions | p. 118 |
| Fractal properties of chaotic motion | p. 125 |
| Transition to chaos | p. 128 |
| Bifurcations of homoclinic and heteroclinic orbits | p. 139 |
| Theoretical predictive criteria of chaos | p. 144 |
| Analysis of time series | p. 146 |
| Time histories and Fourier spectra | p. 148 |
| The pseudo-state space and embedding | p. 158 |
| The embedding dimension and the time delay | p. 162 |
| Regular and irregular motion in Hamiltonian systems | p. 168 |
| Properties of Hamiltonian systems | p. 169 |
| Integrable systems | p. 180 |
| Nearly integrable systems and the KAM theorem | p. 185 |
| Chaos in Hamiltonian systems | p. 191 |
| Extended systems - instabilities and patterns | p. 201 |
| Linear instabilities | p. 205 |
| General qualitative properties of pattern-forming systems | p. 209 |
| Amplitude and envelope equations | p. 212 |
| Phase equations and coherent structures | p. 221 |
| Defects and spatio-temporal complexity in 1D systems | p. 227 |
| Defects in multidimensional systems | p. 243 |
| Coupled map lattices | p. 251 |
| Astrophysical applications | p. 255 |
| Introduction to Part II | p. 257 |
| Planetary, stellar and galactic dynamics | p. 260 |
| The n-body problem - a historical note | p. 262 |
| Chaotic dynamics in the Solar System | p. 267 |
| Chaos and the evolution of tidal-capture binaries | p. 299 |
| The role of chaos in stellar and galactic dynamics | p. 305 |
| Irregularly variable astronomical point sources | p. 317 |
| Observed aperiodic astronomical signals | p. 319 |
| Nonlinear stellar pulsators - some specific models | p. 328 |
| A dynamical-system approach to stellar pulsation | p. 332 |
| Some models of accreting systems | p. 340 |
| Complex spatial patterns in astrophysics | p. 347 |
| Spatial structures in the interstellar medium | p. 348 |
| The large-scale structure of the Universe | p. 370 |
| Topics in astrophysical fluid dynamics | p. 381 |
| Basic concepts and equations | p. 383 |
| Special flows and their properties | p. 392 |
| Hydrodynamical stability | p. 404 |
| Thermal convection and the Lorentz model | p. 422 |
| Hamiltonian formulations and related topics | p. 431 |
| References | p. 444 |
| Index | p. 451 |
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