Genericity of nondegenerate critical points and Morse geodesic functionals Leonardo BiliottiMiquel Angel JavaloyesPaolo Piccione 57R4557R7057N7558E10generic properties of geodesic flows We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [B. White, \textit{The space of minimal submanifolds for varying Riemannian metrics}, Indiana Univ. Math. J. \textbf{40} (1991), 161-200]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3642 10.1512/iumj.2009.58.3642 en Indiana Univ. Math. J. 58 (2009) 1797 - 1830 state-of-the-art mathematics http://iumj.org/access/