N.I. Chernov
On Sinai-Bowen-Ruelle measures on horocycles of 3-D Anosov flows
(30K, LATeX)
ABSTRACT. Let $\phi^t$ be a topologically mixing Anosov flow on a 3-D compact
manifolds $M$. Every unstable fiber (horocycle) of such a flow is
dense in $M$. Sinai proved in 1992 that the one-dimensional SBR
measures on long segments of unstable fibers converge uniformly
to the SBR measure of the flow. We establish an explicit bound
on the rate of convergence in terms of integrals of H\"older
continuous functions on $M$.