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A pseudorandom point in an ergodic dynamical system over a computable metricspace is a point which is computable but its dynamics has the same statisticalbehavior as a typical point of the system.  It was proved in [Avigad et al. 2010, Local stability of ergodic averages]that in a system whose dynamics is computable the ergodic averages ofcomputable observables converge effectively. We give an alternative, simplerproof of this result.  This implies that if also the invariant measure is computable then thepseudorandom points are a set which is dense (hence nonempty) on the support ofthe invariant measure.

Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems