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  "body": "\n## Summary\n\nA Sinai–Ruelle–Bowen measure, or SRB measure, is an [[invariant measure|B232EZ1FMB]] of a smooth dynamical system that is smooth along the expanding directions.\nSuch measures exist for many [[attractors|7FWX24X5MW]] that have zero volume, where no invariant measure can be absolutely continuous.\nThey are the natural measures to observe.\nTake a uniformly hyperbolic attractor.\nFor almost every initial point of its basin, in the sense of volume, the time averages equal the SRB space averages.\n\n## Explanations\n\n### L1 human\n\nRun a chaotic system on a computer from a random starting point and record how often the orbit visits each region.\nThe histogram usually settles down to the same limit for almost every start; that limit is the SRB measure.\nOn a strange attractor the measure lives on a set of zero volume, so it is not given by a density in space.\nAlong the stretched directions, however, it looks like length or area with a density.\nFor [[Arnold's cat map|BSCZN8Y1AN]] the SRB measure is plain area on the torus.\n",
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