The rectangular billiard, with dimension , has four rounded corners (with radius R, see magnification of just one border). The escape point with aperture a lies exactly in the middle of the billiard. Initial angle and, schematically, the shortest escape trajectories ( , and ) are shown. In all simulations, we use L = 4 and D = 10.
Phase-space dynamics for (a) R = 0 and (b) R/L = 0.1 (one IC): Green (light gray) points occur when the trajectory collides with the rounded corner and defines the SR or chaotic region. Blue (dark gray) points occur when the trajectory collides with the vertical and horizontal parallel walls.
(a) Escape angle as a function of and , (b) and (c) are magnifications.
Semi-log plot of for distinct values of R/L. Each curve was obtained using ICs.
Grid of points with the FTLEs as a function of .
FTLEs in the phase space projection for K = 0.15 [see white dashed line in Fig. 5(a) ].
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