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  "body": "\n## Summary\n\nA continuous map is topologically transitive when it carries every nonempty open set, at some time, into every other nonempty open set.\nOn a compact metric space without isolated points this is the same as having a point whose orbit is [[dense|0BSJSX7ME2]].\nA transitive system cannot be split into two open invariant pieces, so it is the topological analogue of an [[ergodic transformation|AZRPHS478B]].\nTransitivity is one of the three conditions in Devaney's definition of chaos.\n\n## Explanations\n\n### L1 human\n\nPick any two regions of the space, however small.\nA transitive map, applied often enough, moves some point of the first region into the second.\nSo the motion links every part of the space with every other part.\nA rotation of a circle by an irrational angle is transitive: every orbit winds around densely.\nThe identity map of an interval is not: nothing ever moves from one region to another.\n",
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