Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T04:14:21.761Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of the weak Pinsker property for flows

Published online by Cambridge University Press:  19 September 2008

Adam Fieldsteel
Adam Fieldsteel
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06457, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An ergodic flow is said to have the weak Pinsker property if it admits a decreasing sequence of factors whose entropies tend to zero and each of which has a Bernoulli complement. We show that this property is preserved under taking factors and d-limits. In addition, we show that a flow has the weak Pinsker property whenever one ergodic transformation in the flow has this property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 3 , September 1984 , pp. 381 - 390
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Fieldsteel, A.. The relative isomorphism theorem for Bernoulli flows. Israel J. Math., 40 (1981), 197–216.CrossRefGoogle Scholar
[2]Ornstein, D. S.. Ergodic Theory, Randomness, and Dynamical Systems. Yale University Press: New Haven and London, 1974.Google Scholar
[3]Thouvenot, J. -P.. Quelques propriétés des systèmes dynamique qui se décomposent en un produit de deux systèmes dout l'un est un schème de Bernoulli. Israel J. Math., 21 (1975), 177–203.CrossRefGoogle Scholar
[4]Thouvenot, J. -P.. Remarques sur les systèmes dynamiques donnes avec plusieurs facteurs. Israel J. Math., 21 (1975), 215–230.CrossRefGoogle Scholar
[5]Thouvenot, J.-P.. On the stability of the weaker Pinsker property. Israel J. Math., 27 (1977), 150–162.CrossRefGoogle Scholar