Detection of the chaotic behaviour of a bouncing ball by the 0–1 test

We examine the two-dimensional map of a bouncing ball system. To distinguish between periodic and chaotic solutions we propose the 0–1 test. This method is based on the spectral properties of chaotic system quantifying the system response: 0 for the regular and 1 for the chaotic solution. The obtained results have been confirmed by the calculation of the maximal Lyapunov exponent defined by the product of Jacobian matrices calculated along corresponding trajectories.