  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.
