We consider dispersing billiard tables whose boundary is piecewise smooth and the free flight function is unbounded. We also assume there are no cusps. Such billiard tables are called type D in the monograph of Chernov and Markarian [
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Figure 4. Singularity structure near type 3 and type 1 boundary points Similar figures can be found in [4,Figure 11]. An unstable curve is indicated with bold on both panels
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A scatterer with a convex corner point (left) and a concave corner point (right)
A simple corridor bounded by two corner points
Singular trajectories after a long flight. The trajectory on the top panel is tangent to the scatterer on the left and the trajectory on the bottom panel is tangent to the scatterer on the right. A neighborhood of the first collision point is magnified for better visibility
Singularity structure near type 3 and type 1 boundary points Similar figures can be found in [4,Figure 11]. An unstable curve is indicated with bold on both panels