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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010123664 | QB466.C45 R43 2006 | Open Access Book | Book | Searching... |
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Summary
Summary
The discipline of nonlinear dynamics has developed explosively in all areas of physics. This comprehensive primer summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Regev demonstrates the possible application of ideas including strange attractors, Poincaré sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems. This self-contained text will appeal to a broad audience of astrophysicists and astronomers who wish to understand and apply modern dynamical approaches to the problems they are working on. It provides researchers and graduate students with the investigative tools they need to fully explore chaotic and complex phenomena.
Table of Contents
| Preface | p. ix |
| Acknowledgements | p. xii |
| Part I Dynamical systems - general | p. 1 |
| 1 Introduction to Part I | p. 3 |
| 2 Astrophysical examples | p. 8 |
| 2.1 Stellar population dynamics | p. 8 |
| 2.2 One-zone model of a nonlinear stellar pulsator | p. 12 |
| 2.3 Stellar orbits in a model galactic potential | p. 21 |
| 2.4 One-element model of thermal convection | p. 28 |
| 2.5 Patterns in a thermally unstable medium | p. 32 |
| 3 Mathematical properties of dynamical systems | p. 40 |
| 3.1 Local geometrical properties | p. 42 |
| 3.2 Global attributes of dynamical systems | p. 71 |
| 3.3 Elements of bifurcation theory | p. 83 |
| 3.4 Dynamical systems near marginality | p. 93 |
| 3.5 Fractal sets and dimensions | p. 102 |
| 4 Properties of chaotic dynamics | p. 112 |
| 4.1 Strange attractors | p. 113 |
| 4.2 Sensitivity to initial conditions | p. 118 |
| 4.3 Fractal properties of chaotic motion | p. 125 |
| 4.4 Transition to chaos | p. 128 |
| 4.5 Bifurcations of homoclinic and heteroclinic orbits | p. 139 |
| 4.6 Theoretical predictive criteria of chaos | p. 144 |
| 5 Analysis of time series | p. 146 |
| 5.1 Time histories and Fourier spectra | p. 148 |
| 5.2 The pseudo-state space and embedding | p. 158 |
| 5.3 The embedding dimension and the time delay | p. 162 |
| 6 Regular and irregular motion in Hamiltonian systems | p. 168 |
| 6.1 Properties of Hamiltonian systems | p. 169 |
| 6.2 Integrable systems | p. 180 |
| 6.3 Nearly integrable systems and the KAM theorem | p. 185 |
| 6.4 Chaos in Hamiltonian systems | p. 191 |
| 7 Extended systems - instabilities and patterns | p. 201 |
| 7.1 Linear instabilities | p. 205 |
| 7.2 General qualitative properties of pattern-forming systems | p. 209 |
| 7.3 Amplitude and envelope equations | p. 212 |
| 7.4 Phase equations and coherent structures | p. 221 |
| 7.5 Defects and spatio-temporal complexity in 1D systems | p. 227 |
| 7.6 Defects in multidimensional systems | p. 243 |
| 7.7 Coupled map lattices | p. 251 |
| Part II Astrophysical applications | p. 255 |
| 8 Introduction to Part II | p. 257 |
| 9 Planetary, stellar and galactic dynamics | p. 260 |
| 9.1 The n-body problem - a historical note | p. 262 |
| 9.2 Chaotic dynamics in the Solar System | p. 267 |
| 9.3 Chaos and the evolution of tidal-capture binaries | p. 299 |
| 9.4 The role of chaos in stellar and galactic dynamics | p. 305 |
| 10 Irregularly variable astronomical point sources | p. 317 |
| 10.1 Observed aperiodic astronomical signals | p. 319 |
| 10.2 Nonlinear stellar pulsators - some specific models | p. 328 |
| 10.3 A dynamical-system approach to stellar pulsation | p. 332 |
| 10.4 Some models of accreting systems | p. 340 |
| 11 Complex spatial patterns in astrophysics | p. 347 |
| 11.1 Spatial structures in the interstellar medium | p. 348 |
| 11.2 The large-scale structure of the Universe | p. 370 |
| 12 Topics in astrophysical fluid dynamics | p. 381 |
| 12.1 Basic concepts and equations | p. 383 |
| 12.2 Special flows and their properties | p. 392 |
| 12.3 Hydrodynamical stability | p. 404 |
| 12.4 Thermal convection and the Lorentz model | p. 422 |
| 12.5 Hamiltonian formulations and related topics | p. 431 |
| References | p. 444 |
| Index | p. 451 |
