Geometrical origin of chaoticity in the bouncing ball billiard

We present a study of the chaotic behaviour of the bouncing ball billiard. The work is realised on the purpose of finding at least certain causes of separation of the neighbouring trajectories. Having in view the geometrical construction of the system, we report a clear origin of chaoticity of the bouncing ball billiard. By this we claim that in case when the floor is made of arc of circles – in a certain interval of frequencies – one can give semi-analytical estimates on chaotic behaviour.

► We study the possible separation of neighouring trajectories in the bouncing ball billiard.
► In a certain interval of frequencies semianalitical evaluations are possible.
► One may find a lower bound for the maximal Lyapunov exponent in case of a resonance.