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  "body": "\n## Summary\n\nA smooth dynamical system is a [[dynamical system|BBZP1R872N]] whose phase space is a [[smooth manifold|F45VQ47GPV]] and whose time evolution is differentiable.\nIn discrete time it is a [[diffeomorphism|0KZZ70ZHXP]] iterated forward and backward; in continuous time it is the [[flow|06738GGWWK]] of a smooth vector field.\nDifferentiability allows one to linearise the motion along orbits, which leads to hyperbolicity, invariant manifolds and Lyapunov exponents.\nMost dynamical systems of mechanics and of the sciences are smooth.\n\n## Explanations\n\n### L1 human\n\nA smooth dynamical system is a rule that moves the points of a smooth space, such as a surface, without tearing or creasing it.\nEither the rule is applied in steps, or the points flow continuously along arrows drawn on the space.\nNear each orbit the motion looks, to first order, like a linear map, so tools from linear algebra apply.\nFor example, rotating the circle by a fixed angle, or letting a pendulum swing, are smooth dynamical systems.\nSee the [[definition|HZKFNZTHZS]].\n",
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