Time change for unipotent flows and rigidity

Lindenstrauss, Elon¹ ; Wei, Daren²

¹ Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 9190401, Israel
² Department of Mathematics, National University of Singapore, 119076, Singapore

Mathematics Research Reports, Tome 4 (2023), pp. 11-22

Résumé

We prove a dichotomy regarding the behavior of one-parameter unipotent flows on quotients of semisimple lie groups under time change. We show that if $u_t^{\left(1\right)}$ acting on $G_1/{\Gamma }_1$ is such a flow it satisfies exactly one of the following:

• (1) The flow is loosely Kronecker, and hence isomorphic after an appropriate time change to any other loosely Kronecker system.
• (2) The flow exhibits the following rigid behavior: if the one-parameter unipotent flow $u_t^{\left(1\right)}$ on $G_1/{\Gamma }_1$ is isomorphic after time change to another such flow $u_t^{\left(2\right)}$ on $G_2/{\Gamma }_2$, then $G_1/{\Gamma }_1$ is isomorphic to $G_2/{\Gamma }_2$ with the isomorphism taking $u_t^{\left(1\right)}$ to $u_t^{\left(2\right)}$ and moreover the time change is cohomologous to a trivial one.

The full details will appear in a later publication.

Détail

Reçu le : 2023-01-06
Révisé le : 2023-04-20
Publié le : 2023-09-29

DOI : 10.5802/mrr.15

Classification : 37A17, 37A20, 37A35, 37C10
Keywords: time change, rigidity, unipotent flows, Kakutani equivalence

Licence : CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits