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We give a proof of the existence of generalized definable locally compactmodels for arbitrary approximate subgroups via an application of topologicaldynamics in model theory. Our construction is simpler and shorter than theoriginal one obtained by Hrushovski in ``Beyond the Lascar group'', and it usesonly basic model theory (mostly spaces of types and realizations of types). Themain tools are Ellis groups from topological dynamics considered for suitablespaces of types. However, we need to redevelop some basic theory of topologicaldynamics for suitable ``locally compact flows'' in place of (compact) flows. Wealso prove that the generalized definable locally compact model which weconstructed is universal in an appropriate category. We note that the mainresult yields structural information on definable generic subsets of definablegroups, with a more precise structural result for generics in the universalcover of $\textrm{SL}_2(\mathbb{R})$.

Generalized locally compact models for approximate groups