Chaotic dynamics could not achieve its present status of a fundamental branch of theoretical and experimental research without the invaluable support provided by computers. The possibility of performing long-time numerical integrations of orbits of dynamical systems has allowed us to explore in depth the world of chaos discovered in the pioneering investigations of the start of the century and to greatly expand the realm of non-linear dynamics, especially in the area of dissipative systems. Here we want to sketch some of the issues that arise when performing computer “experiments”, such as the problem of numerical errors and the choice of the integration algorithm. After this, we describe their main contributions to the description of chaos and close with a discussion of the latest findings with respect to the question that can be duly considered central in celestial mechanics, namely the relation between chaoticity and evolution of the N-body gravitating system.
KeywordsSolar System Lyapunov Exponent Chaotic Dynamic Globular Cluster Kepler Problem
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