Comptes Rendus
no. 10
Dynamical Systems
On the conjugacy relation in ergodic theory

Presented by: Gilles Pisier

Matthew D. Foreman1; Daniel J. Rudolph2; Benjamin Weiss3
1 Mathematics Department, UC Irvine, Irvine, CA 92697, USA
2 Mathematics Department, Colorado State University, Fort Collins, CO 80523, USA
3 Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
Comptes Rendus. Mathématique, Volume 343 (2006) no. 10, pp. 653-656.

The set of pairs of transformations on the interval [0,1] can be equipped with a standard Borel structure. We prove that the relation of conjugacy is not a Borel subset of this space, in fact it is complete analytic. Moreover, our construction proves that the two sets, {T:Tis conjugate ofT−1}, and {T:the centralizer ofTis non-trivial} are complete analytic sets.

L'ensemble des paires de transformations ergodiques de l'intervalle [0,1] peut être muni d'une structure borélienne standard. Nous montrons que la relation de conjugaison n'est pas borélienne dans cet espace, en fait est analytique complète. Notre construction montre aussi que les ensembles {T:Test conjugué deT−1} et {T:la centralisateur deTest non-trivial} sont des analytiques complets.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.09.011

Matthew D. Foreman 1; Daniel J. Rudolph 2; Benjamin Weiss 3

1 Mathematics Department, UC Irvine, Irvine, CA 92697, USA
2 Mathematics Department, Colorado State University, Fort Collins, CO 80523, USA
3 Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel 
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Matthew D. Foreman; Daniel J. Rudolph; Benjamin Weiss. On the conjugacy relation in ergodic theory. Comptes Rendus. Mathématique, Volume 343 (2006) no. 10, pp. 653-656. doi : 10.1016/j.crma.2006.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.011/

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