Expansiveness and Hyperbolicity in Convex Billiards

We say that a convex planar billiard table $$B$$ is $$C^{2}$$ -stably expansive on fixed open subset $$U$$ of the phase space if its map $$f_{B}$$ maximal invariant set $$\Lambda_{B,U}=\bigcap_{n\in\mathbb{Z}}f^{n}_{B}(U)$$ , and this property holds under -perturbations table. In note we prove for such billiards closure periodic points in $$\Lambda_{B,U}$$ uniformly hyperbolic. addition, show also generic choice among which are expansive.