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  "body": "\n## Summary\n\nA hyperbolic set of a diffeomorphism is a compact invariant set with a splitting of the tangent space at each of its points.\nOne part is uniformly contracted and the other is uniformly expanded.\nIt extends the notion of a hyperbolic fixed point from one point to a whole set, possibly a Cantor set or the whole manifold.\nHyperbolic sets have stable and unstable manifolds, the shadowing property and robustness under perturbation.\nThey are the setting of uniformly hyperbolic dynamics, which includes [[Anosov diffeomorphisms|RCQH8P6DPQ]] and the [[Smale horseshoe|N63Z6EA6YS]].\n\n## Explanations\n\n### L1 human\n\nPicture a map that, near some set of points, squeezes in one direction and stretches in another, at every point of the set and at a uniform rate.\nSuch a set is hyperbolic.\nNearby points drift apart along the stretched direction, so the motion on a large hyperbolic set can be chaotic, yet the clear geometry makes it possible to analyse.\nThe simplest case is a single saddle point, such as the origin for the map $(x, y) \\mapsto (x/2, 2y)$.\nSee the [[definition|NY9MCZXY6N]].\n",
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