### Resumen

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 [2] 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.

Idioma original | English |
---|---|

Páginas (desde-hasta) | 7-18 |

Número de páginas | 12 |

Publicación | Electronic Proceedings in Theoretical Computer Science, EPTCS |

Volumen | 24 |

DOI | |

Estado | Published - 2010 |

### Huella dactilar

### ASJC Scopus subject areas

- Software

### Citar esto

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*Electronic Proceedings in Theoretical Computer Science, EPTCS*, vol. 24, pp. 7-18. https://doi.org/10.4204/EPTCS.24.6

**Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems.** / Galatolo, Stefano; Hoyrup, Mathieu; Rojas, Crist́obal.

Resultado de la investigación: Article

TY - JOUR

T1 - Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems

AU - Galatolo, Stefano

AU - Hoyrup, Mathieu

AU - Rojas, Crist́obal

PY - 2010

Y1 - 2010

N2 - 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 [2] 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.

AB - 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 [2] 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.

UR - http://www.scopus.com/inward/record.url?scp=84885594748&partnerID=8YFLogxK

U2 - 10.4204/EPTCS.24.6

DO - 10.4204/EPTCS.24.6

M3 - Article

AN - SCOPUS:84885594748

VL - 24

SP - 7

EP - 18

JO - Electronic Proceedings in Theoretical Computer Science, EPTCS

JF - Electronic Proceedings in Theoretical Computer Science, EPTCS

SN - 2075-2180

ER -