Abstract
A classical consequence of KAM theory is that if γ is a smooth strictly convex curve then neither inner nor outer billiard orbits can accumulate on γ. On the other hand several authors observed that this result is false in general if γ is not smooth (or if it is not strictly convex). In this paper we consider piecewise smooth strictly convex curves with curvature jump discontinuities and estimate the diffusion speed for those curves. Namely, we show that both inner and outer billiard maps for γ have orbits which approach γ with speed 1/m2.
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