The theory of dynamical systems, or mappings, plays an important role in various disciplines of modern physics, including celestial mechanics and fluid mechanics. This comprehensive introduction to the general study of mappings has particular emphasis on their applications to the dynamics of the solar system. The book forms a bridge between continuous systems, which are suited to analytical developments and to discrete systems, which are suitable for numerical exploration.
Featuring chapters based on lectures delivered at the School on Discrete Dynamical Systems (Aussois, France, February 1996) the book contains three parts - Numerical Tools and Modelling, Analytical Methods, and Examples of Application. It provides a single source of information that, until now, has been available only in widely dispersed journal articles.
1. Part I: Modelling Mappings: An Aim and a Tool for the Study of Dynamical Systems 2. Spectra of Stretching Numbers and Helicity Angles 3. Diffusion and Transient Spectra in a 4-Dimensional Symplectic Mapping 4. Distribution of Periodic Orbits in 2-D Dynamical Systems 5. Symplectic Integrators 6. The Use of Mappings for Stability Problems in Beam Dynamics 7. Part II: Rigorous and Numerical Determination of Rotational Invariant Curves for the Standard Map 8. Interpolation of Discrete Hamiltonian Systems 9. Standard and Anomalous Diffusion in Dynamical Systems 10. Part III: Symplectic Maps and Their Use in Celestial Mechanics 11. Perturbation Theory for Volume Preserving Maps: Application to the Magnetic Field Lines in Plasma Physics