Deviations for generalized tiling billiards in cyclic polygons
Résumé
This work continues the study of tiling billiards, a class of dynamical system
introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards
in a cyclic polygon. This work shows that the behavior of generalized tiling billiards in
cyclic N-gons with N > 4 is considerably different from that of triangular and quadrilateral
tiling billiards studied before. Indeed, we exhibit an open set of generalized tiling billiard
trajectories deviating sublinearly from their asymptotic direction, whereas for N = 3 or 4
almost every trajectory stays at a bounded distance from a line. Moreover, we establish the
rate of deviations both in the generic case and in some non generic cases.
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