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  "body": "\n## Summary\n\nThe non-wandering set of a continuous map consists of the points $x$ whose every neighbourhood meets one of its own later images.\nIt is the complement of the set of wandering points from the notion of [[wandering set|VNW5FHCQ2M]].\nIt is closed and invariant, and it contains every [[periodic orbit|0AA97XA70K]], every [[recurrent point|4SQHHRPKMV]] and every $\\omega$-[[limit set|YF4XH2BEG5]].\nIn smooth dynamics, hyperbolicity conditions such as Smale's Axiom A are imposed on the non-wandering set.\n\n## Explanations\n\n### L1 human\n\nSome points of a system are only passing through: a small region around them drifts away and never overlaps itself again.\nThe non-wandering set is what is left when all such passing points are removed.\nIt is where the motion keeps coming back to, so it holds all the long-term behaviour.\nFor a pendulum with friction, only the rest positions are non-wandering; every other state slowly drifts toward rest.\n",
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