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

2 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
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.
Type de document :
Communication dans un congrès
Xizhong Zheng and Ning Zhong. Computability and Complexity in Analysis (CCA), Jun 2010, Zhenjiang, China. 24, pp.7-18, 2010, Electronic Proceedings in Theoretical Computer Science. 〈http://arxiv.org/abs/1006.0392v1〉. 〈10.4204/EPTCS.24.6〉
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Littérature citée [17 références]

https://hal.inria.fr/inria-00517372
Contributeur : Mathieu Hoyrup <>
Soumis le : mardi 14 septembre 2010 - 14:18:15
Dernière modification le : jeudi 11 janvier 2018 - 06:21:25
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1006.0392v1.pdf
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Stefano Galatolo, Mathieu Hoyrup, Cristobal Rojas. Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems. Xizhong Zheng and Ning Zhong. Computability and Complexity in Analysis (CCA), Jun 2010, Zhenjiang, China. 24, pp.7-18, 2010, Electronic Proceedings in Theoretical Computer Science. 〈http://arxiv.org/abs/1006.0392v1〉. 〈10.4204/EPTCS.24.6〉. 〈inria-00517372〉

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