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  "body": "\n## Summary\n\nAn Anosov diffeomorphism is a diffeomorphism of a compact manifold for which the whole manifold is a [[hyperbolic set|MPFD24TYW2]].\nAt every point it contracts some directions and expands the complementary ones, uniformly.\nAnosov diffeomorphisms are [[structurally stable|D4MGFAHVMT]], satisfy [[Axiom A|Z26Z4XZFVA]] and admit [[Markov partitions|4VNHVDHTNN]].\nThe basic examples are the hyperbolic toral automorphisms, such as [[Arnold's cat map|BSCZN8Y1AN]].\n\n## Explanations\n\n### L1 human\n\nTake a torus and a map that stretches it in one direction and squeezes it in another, everywhere and by a fixed rate.\nSuch a map mixes points very fast, like dough being kneaded, but it never tears the surface.\nArnold's cat map, given by the matrix with rows $(2, 1)$ and $(1, 1)$ acting on the torus, is the standard example.\nSmall smooth changes of an Anosov diffeomorphism do not change its orbit structure.\nSee the [[definition|X1P48KQFXQ]].\n",
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