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We introduce dynamic asymptotic dimension, a notion of dimension for actionsof discrete groups on locally compact spaces, and more generally for locallycompact \'etale groupoids. We study our notion for minimal actions of theinteger group, its relation with conditions used by Bartels, L\"uck, and Reichin the context of controlled topology, and its connections with Gromov's theoryof asymptotic dimension. We also show that dynamic asymptotic dimension givesbounds on the nuclear dimension of Winter and Zacharias for C*-algebrasassociated to dynamical systems. Dynamic asymptotic dimension also hasimplications for K-theory and manifold topology: these will be drawn out insubsequent work.

Dynamic Asymptotic Dimension: relation to dynamics, topology, coarse geometry, and $C^*$-algebras