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  "body": "\n## Summary\n\nA Markov partition of a hyperbolic system is a cover of the space by finitely many pieces, called rectangles.\nThe map moves these rectangles in a very regular way.\nEach rectangle is a product of a stable and an unstable piece, and the map stretches the unstable pieces across whole rectangles.\nRecording which rectangle a point visits at each time turns the system into a [[subshift of finite type|624XDXX8FN]].\nIn this way Markov partitions make [[symbolic dynamics|EWFWTSVY0B]] a tool for [[Anosov diffeomorphisms|RCQH8P6DPQ]] and for the basic sets of [[Axiom A|Z26Z4XZFVA]] systems.\n\n## Explanations\n\n### L1 human\n\nCut the space into a few boxes, and name each box by a letter.\nFollow a point under the map and write down the letter of the box it is in at each time.\nFor a Markov partition the boxes are chosen so well that the allowed strings of letters are exactly those that avoid a finite list of forbidden pairs.\nSo the complicated motion is described by a simple rule on sequences of letters.\nFor the [[Smale horseshoe|N63Z6EA6YS]], two boxes already suffice, and every sequence of two letters occurs.\nSee the [[definition|3S543TYT8C]].\n",
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