On Sinai-bowen-ruelle Measures on Horocycles of 3-d Anosov Ows

Abstract

Let t be a topologically mixing Anosov ow on a 3-D compact manifolds M. Every unstable ber (horocycle) of such a ow is dense in M. Sinai proved in 1992 that the one-dimensional SBR measures on long segments of unstable bers converge uniformly to the SBR measure of the ow. We establish an explicit bound on the rate of convergence in terms of integrals of HH older continuous functions on M.

Cite this paper

@inproceedings{Chernov1997OnSM, title={On Sinai-bowen-ruelle Measures on Horocycles of 3-d Anosov Ows}, author={Nikolai I. Chernov}, year={1997} }