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We provide a framework for studying the expansion rate of the image of abounded set under a flow in Euclidean space and apply it to stochasticdifferential equations (SDEs for short) with singular coefficients. If thesingular drift of the SDE can be split into two terms, one of which is singularand the radial component of the other term has a radial component of sufficientstrength in the direction of the origin, then the random dynamical systemgenerated by the SDE admits a pullback attractor.

Expansion and attraction of RDS: long time behavior of the solution to singular SDE