TY - JOUR
T1 - On the ergodic properties of Cartan flows in ergodic actions of SL2(R) and SO(n, 1)
AU - Furman, Alex
AU - Weiss, Benjamin
PY - 1997/12
Y1 - 1997/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0031317081&partnerID=8YFLogxK
U2 - 10.1017/S0143385797097629
DO - 10.1017/S0143385797097629
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AN - SCOPUS:0031317081
SN - 0143-3857
VL - 17
SP - 1371
EP - 1382
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 6
ER -