On the ergodic properties of Cartan flows in ergodic actions of SL2(R) and SO(n, 1)

Alex Furman*, Benjamin Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let G = SL2(R) (or G = SO(n, 1)) act ergodically on a probability space (X, m). We consider the ergodic properties of the flow (X, m, {g,}), where {gt} is a Cartan subgroup of G. The geodesic flow on a compact Riemann surface is an example of such a flow; here X = G/ Γ is a transitive G-space, G = SL2(R) and Γ ⊂ G is a lattice. In this case the flow is Bernoullian. For the general ergodic G-action, the flow (X, m, {gt}) is always a K-flow, however there are examples in which it is not Bernoullian.

Original languageEnglish
Pages (from-to)1371-1382
Number of pages12
JournalErgodic Theory and Dynamical Systems
Volume17
Issue number6
DOIs
StatePublished - Dec 1997

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