Under computable compactness and overtness of invariant measures, the max ergodic average of a computable potential is computable and maximising measures form a Π1 set; for finite-range SFT potentials an explicit max-mean-cycle algorithm computes both exactly.
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Computable Ergodic Optimisation
Under computable compactness and overtness of invariant measures, the max ergodic average of a computable potential is computable and maximising measures form a Π1 set; for finite-range SFT potentials an explicit max-mean-cycle algorithm computes both exactly.