Abstract
This paper is devoted to the effective stability estimates (of Nekhoroshev’s type) of the billiard flow for strictly convex bounded domains with analytic boundaries in any dimensions. The main result is that any billiard trajectory with initial data which are δ - close to the glancing manifold remains close to the glancing manifold in an exponentially large time interval with respect to 1/δ. The proof is based on a normal form of the billiard ball map in Gevrey classes. More generally, we prove effective stability estimates for the billiard ball map associated with any pair of analytic glancing hypersurfaces with a compact glancing manifold.
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