Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T01:12:47.967Z Has data issue: false hasContentIssue false
  • English
  • Français

On the ergodic properties of Cartan flows in ergodicactions of ${\bf SL}_{\bf 2}{\bf (R)}$ and ${\bf SO}{\bf ({\bi n},1)}$

Published online by Cambridge University Press:  01 December 1997

ALEX FURMAN  and
BENJAMIN WEISS
ALEX FURMAN
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem, 91904 Israel (e-mail: [email protected]) (e-mail: [email protected]) Current address: Department of Mathematics, Penn State University, 218 McAllister Building, University Park, PA 16802, USA.
BENJAMIN WEISS
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem, 91904 Israel (e-mail: [email protected]) (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Let $G={\rm SL_2({\bf R})}$ (or $G={\rm SO}(n,1)$) act ergodically on a probability space $(X,m)$. We consider the ergodic properties of the flow $(X,m,\{g_t\})$, where $\{g_t\}$ is a Cartan subgroup of $G$. The geodesic flow on a compact Riemann surface is an example of such a flow; here $X=G/\Gamma$ is a transitive $G$-space, $G={\rm SL_2({\bf R})}$ and $\Gamma\subset G$ is a lattice. In this case the flow is Bernoullian.

For the general ergodic $G$-action, the flow $(X,m,\{g_t\})$ is always a $K$-flow, however there are examples in which it is not Bernoullian.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 6 , December 1997 , pp. 1371 - 1382
Copyright
1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)