Assume that there is a collection of semi-circles of diameter 1 in the upper half plane centered at the integer points (n,0) on the x-axis. A released billiard ball falls down under the vertical constant gravitational force g. The ball bounces off the semi-circles according to the billiard law and describes a trajectory γ. Record the indices of the semi-circles the ball hits as a sequence
ω = (ω1, ω2, ...),
which we call the one-sided itinerary of the trajectory γ. We will investigate this dynamical system.
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