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  "body": "\n## Summary\n\nAn expansive homeomorphism is a [[homeomorphism|0QT00PB5G2]] of a metric space that separates any two distinct points by a fixed distance at some time.\nThis time may lie in the past or in the future.\nThe fixed distance is the expansivity constant.\nShift spaces and Anosov diffeomorphisms are the basic examples.\nOn a compact metric space, an expansive homeomorphism has finite [[topological entropy|BDZYBXBFDE]] and at most finitely many periodic points of each period.\n\n## Explanations\n\n### L1 human\n\nTwo different starting points can look the same for a while, but an expansive map never lets them stay close forever.\nAt some moment, forward or backward in time, they are at least a fixed distance apart.\nSo with a fixed precision one can tell every orbit apart from every other one by watching the whole history.\nIn a shift space of two-sided sequences, two different sequences differ at some position, and shifting that position to the centre makes them far apart.\nA rotation of the circle is not expansive, because it keeps all distances unchanged.\n",
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