The discipline of nonlinear dynamics has developed explosively in all areas of physics. This comprehensive primer, first published in 2006, 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.
• Includes a comprehensive and self-contained introduction to dynamical system and pattern theory, especially appropriate for astrophysicists • Uses examples to demonstrate theoretical notions in astronomy and astrophysics whenever possible • Gives many diverse applications of chaos and complexity theory to astrophysics, and discusses them in considerable detail
Contents
Part I. Dynamical Systems - General: 1. Introduction to Part I; 2. Astrophysical examples; 3. Mathematical properties of dynamical systems; 4. Properties of chaotic dynamics; 5. Analysis of time series; 6. Regular and irregular motion in Hamiltonian systems; 7. Extended systems - instabilities and patterns; Part II. Astrophysical Applications: 8. Introduction to Part II; 9. Planetary, stellar and galactic dynamics; 10. Irregularly variable astronomical point sources; 11. Complex spatial patterns in astrophysics; 12. Topics in astrophysical fluid dynamics; References; Index.
Review
Review of the hardback: 'There are countless books on dynamical systems, chaos, nonlinear dynamics, and so on, but this is the best for the all-round astrophysicist. It is not a straight-laced textbook or a how-to manual, but a good-natured guidebook to the literature. … you will end up much better educated, learning lots of facts and insights into a wide range of topics from Liapounov indicators to the theory of turbulence. … Without eschewing deep results, the book is as readable as a novel, and like any decent novel, deserves to be read from cover to cover …' The Observatory
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