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Using tools from computable analysis we develop a notion of effectiveness forgeneral dynamical systems as those group actions on arbitrary spaces thatcontain a computable representative in their topological conjugacy class. Mostnatural systems one can think of are effective in this sense, including somegroup rotations, affine actions on the torus and finitely presented algebraicactions. We show that for finitely generated and recursively presented groups,every effective dynamical system is the topological factor of a computableaction on an effectively closed subset of the Cantor space. We then apply thisresult to extend the simulation results available in the literature beyondzero-dimensional spaces. In particular, we show that for a large class ofgroups, many of these natural actions are topological factors of subshifts offinite type.

Effective dynamical systems beyond dimension zero and factors of SFTs