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Abstract
The global properties of attractors of a class of dynamical systems are studied in the state space. The concept of real-time attractor is introduced with the view on practical applications. The abstract properties of attractors and real-time attractors are illustrated on classical examples in mechanics by computing the domains of attraction of asymptotically stable equilibria and periodic solutions using the method of point mapping. The properties of transient attractors are also studied. One of the possible applications here is to use them in generating the map of a differential game in the state space