The singularities of a dynamical system are usually its equilibrium points. They are heavily studied by the mathematicians, partly because there is a lack of global methods to study the dynamical systems far from their equilibrium points or periodic solutions. But there is much more to this. The singularities and periodic orbits organize the global dynamics. This statement will be illustrated with examples within mathematics and from other sciences, mainly celestial mechanics and the n-body problem.

 

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