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  "body": "\n## Summary\n\nA diffeomorphism satisfies Axiom A if its [[non-wandering set|EY2W34JZA4]] is a [[hyperbolic set|MPFD24TYW2]] in which periodic points are dense.\nSmale introduced the condition to single out a large class of systems whose dynamics can be described completely.\nFor such systems the non-wandering set splits into finitely many basic pieces by the [[spectral decomposition theorem|6MTVY6NYY7]].\nEach piece is coded by a [[subshift of finite type|624XDXX8FN]].\n[[Anosov diffeomorphisms|RCQH8P6DPQ]], [[Morse–Smale systems|7AMQ8GS78Y]] and the [[Smale horseshoe|N63Z6EA6YS]] satisfy Axiom A.\n\n## Explanations\n\n### L1 human\n\nMost points of a dynamical system wander off and never come back near where they started.\nThe interesting dynamics happens on the set of points that keep returning, the non-wandering set.\nAxiom A asks that on this set the system stretches and squeezes uniformly, and that periodic orbits are everywhere in it.\nThen the long-term behaviour can be cut into finitely many pieces, each understood by symbolic codes.\nSee the [[definition|S31RTTJPDC]].\n",
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