Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systemsReport as inadecuate




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1 DMA - Dipartimento di Matematica Applicata Pisa 2 CARTE - Theoretical adverse computations, and safety Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods 3 Department of Mathematics - University of Toronto

Abstract : A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in J. Avigad, P. Gerhardy, H. Towsner. Local stability of ergodic averages that in a system whose dynamics is computable the ergodic averages of computable observables converge effectively. We give an alternative, simpler proof of this result. This implies that if also the invariant measure is computable then the pseudorandom points are a set which is dense hence nonempty on the support of the invariant measure.





Author: Stefano Galatolo - Mathieu Hoyrup - Cristobal Rojas -

Source: https://hal.archives-ouvertes.fr/



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