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Here we investigate the question of what dynamical systems can be written as quotients of $\\mathbb{N}^*$. We prove that a dynamical system is a quotient of $\\mathbb{N}^*$ if and only if it is isomorphic to the $\\omega$-limit set of some point in some larger system. This provides a full external characterization of the quotients of $\\mathbb{N}^*$. 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