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

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.
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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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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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