Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download

https://hal.inria.fr/inria-00517372
Contributor : Mathieu Hoyrup Connect in order to contact the contributor
Submitted on : Tuesday, September 14, 2010 - 2:18:15 PM
Last modification on : Wednesday, May 4, 2022 - 3:14:21 AM
Long-term archiving on: : Wednesday, December 15, 2010 - 2:45:31 AM

File

1006.0392v1.pdf
Publisher files allowed on an open archive

Identifiers

Citation

Stefano Galatolo, Mathieu Hoyrup, Cristobal Rojas. Computing the speed of convergence of ergodic averages and pseudorandom points in computable dynamical systems. Computability and Complexity in Analysis (CCA), Jun 2010, Zhenjiang, China. pp.7-18, ⟨10.4204/EPTCS.24.6⟩. ⟨inria-00517372⟩

Share

Metrics

Record views

185

Files downloads

115