On Sinai-Bowen-Ruelle measures on horocycles of 3-D Anosov flows. (English) Zbl 0898.58042
From the abstract: “Let \(\phi^t\) be a topologically mixing Anosov flow on a 3-dimensional compact manifold \(M\). 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 Hölder continuous functions on \(M\)”.
Reviewer: Raul Ibañez (Bilbão)
MSC:
37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
53D25 | Geodesic flows in symplectic geometry and contact geometry |
37E99 | Low-dimensional dynamical systems |
37A99 | Ergodic theory |