Real-analytic perturbation of the Euclidean hypersurface yields generic nondegeneracy of closed geodesics and Kupka-Smale transversality, and on strictly convex surfaces in R3 a transverse homoclinic orbit is C^omega-generic.
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Generic Properties of Geodesic Flows on Analytic Hypersurfaces of Euclidean Space
Real-analytic perturbation of the Euclidean hypersurface yields generic nondegeneracy of closed geodesics and Kupka-Smale transversality, and on strictly convex surfaces in R3 a transverse homoclinic orbit is C^omega-generic.