Pseudoconvex and Disprisoning Homogeneous Sprays
  The pseudoconvex and disprisoning conditions for geodesics of linear connections are extended to the solution curves of general homogeneous sprays. The main result is that pseudoconvexity and disprisonment are jointly stable in the fine topology on the space of all homogeneous sprays of any degree of homogeneity. 
L. Del Riego and P.E. Parker