Bessa, MárioDias, João LopesMatias, PedroTorres, Maria JoanaWenxian , Shen2025-10-272025-10-2720250002-9939http://hdl.handle.net/10400.2/20394We consider a semi-Riemannian metric whose associated geodesic flow either contains a non-hyperbolic periodic orbit or has infinitely many hyperbolic periodic orbits. Under some conditions, we show that the metric can be perturbed such that the geodesic flow exhibits positive topological entropy, there are infinitely many non-lightlike closed geodesics, and their number grows exponentially with respect to the length.engSemi-Riemannian manifoldsClosed geodesicsTopological entropyHyperbolic setsjournal article10.1090/proc/173371088-6826