Transition to chaos and basins of attraction in the impact oscillator

The impact oscillator is the simplest mechanical system with the strong nonlinearity, which is caused by a sudden change of stiffness during the contact of impacting bodies. When the time duration of the impact is assumed negligibly short, then the Newton elementary theory of impact can be used for the investigation of the system dynamics. The paper introduces a short review of results, explains the substance of different ways from periodic to chaotic impact motions, and shows the basins of attraction in the manifold response of the system.