Continuity and collapse of geodesic patterns of flows on surfaces (Q1594131)

The authors state without proof some results about the relation between the orbit structure of a smooth flow on a closed surface \(S\) on genus \(g\geq 2\) and geodesic laminations on \(S\). Their main interest lies in flows whose 1-dimensional trajectories are dense on \(S\) and whose zeros are hyperbolic saddle points. To such flow corresponds a geodesic lamination which depends continuously on a closed subset of \(S\) on the generator of the flow in the \(C^1\)-topology.