Analysis and Modelling of Discrete Dynamical Systems

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Daniel Benest, Claude Froeschle
CRC Press, Oct 28, 1998 - Computers - 344 pages
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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.
 

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Contents

Spectra of Stretching Numbers and Helicity Angles
55
Diffusion and Transient Spectra in a 4Dimensional
91
Distribution of Periodic Orbits in 2D Dynamical Systems
107
Symplectic Integrators
133
Rigorous and Numerical Determination of Rotational
149
Interpolation of Discrete Hamiltonian Systems
181
Standard and Anomalous Diffusion in Dynamical Systems
229
Part HI Examples of Application
249
The Use of Mappings for Stability Problems in Beam Dynamics
301
Index
315
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