In joint work with Inmaculada Baldoma, Anna Florio, and Tere M. Seara, we demonstrate that a generic analytic strongly convex billiard is "maximally chaotic", i.e., for every rational number p/q in the intersection of the rationals with (0,1), all intersections between the stable and unstable manifolds of periodic orbits in the Aubry-Mather set with rotation number p/q are transverse. More recently, we extended this study to verify that a generic analytic strongly convex billiard satisfies the Kupka-Smale property.