On the ergodic properties of Cartan flows in ergodic actions of SL(2,R) and SO(n,1)

Let G=SL(2,**R**), or SO(n,1) or SU(n,1) act ergodically
on a probability space (X,m). Consider the ergodic properties of the flow
(X,m,{g_t}), where {g_t} is a Cartan subgroup of G. The geodesic flow on
the (frame bundle) of a compact (real or complex) hyperbolic manifold is
an example of such flow, here X=G/L is a transitive G-space, G=SO(n,1)
or SU(n,1) and L is a lattice in G. In this case the flow is known to be
Bernoullian.

For the general ergodic G-action, the flow (X,m,{g_t}) is always a
K-flow. We construct examples where such flows are not Bernoullian. (In
the paper we discuss the groups SO(n,1), however the constructions and
the proofs apply to SU(n,1) as well).

Bibliographical: Ergodic Theory Dynam. Systems

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[Papers] [Alex Furman]