Statistical Behaviour of the Leaves of Riccati Foliations
| dc.creator | Bonatti, Ch. | |
| dc.creator | Gomez-Mont, X. | |
| dc.creator | Vila-Freyer, R. | |
| dc.date | 2008-06-18 | |
| dc.date.accessioned | 2026-07-07T09:45:18Z | |
| dc.date.available | 2026-07-07T09:45:18Z | |
| dc.description | We introduce the geodesic flow on the leaves of a holomorphic foliation with leaves of dimension 1 and hyperbolic, corresponding to the unique complete metric of curvature -1 compatible with its conformal structure. We do these for the foliations associated to Riccati equations, which are the projectivisation of the solutions of linear ordinary differential equations over a finite Riemann surface of hyperbolic type S, and may be described by a representation r:pi_1(S) -> GL(n,C). We give conditions under which the foliated geodesic flow has a generic repellor-attractor statistical dynamics. That is, there are measures m- and m+ such that for almost any initial condition with respect to the Lebesgue measure class the statistical average of the foliated geodesic flow converges for negative time to m- and for positive time to m+ (i.e. m+ is the unique SRB-measure and its basin has total Lebesgue measure). These measures are ergodic with respect to the foliated geodesic flow. These measures are also invariant under a foliated horocycle flow and they project to a harmonic measure for the Riccati foliation, which plays the role of an attractor for the statistical behavior of the leaves of the foliation. | |
| dc.identifier | https://arxiv.org/abs/0806.2894 | |
| dc.identifier | http://arxiv.org/abs/0806.2894 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163149 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F75, 57R30, 53D25, 37D40, 37H05 | |
| dc.title | Statistical Behaviour of the Leaves of Riccati Foliations | |
| dc.type | text |