Sinai–Ruelle–Bowen measure

Summary

A Sinai–Ruelle–Bowen measure, or SRB measure, is an invariant measure of a smooth dynamical system that is smooth along the expanding directions. Such measures exist for many attractors that have zero volume, where no invariant measure can be absolutely continuous. They are the natural measures to observe. Take a uniformly hyperbolic attractor. For almost every initial point of its basin, in the sense of volume, the time averages equal the SRB space averages.