Periodic Solutions and Chaotic Dynamics in Forced Impact Oscillators

It is shown that a periodically forced impact oscillator may exhibit chaotic dynamics on two symbols, as well as an infinity of periodic solutions. Two cases are considered, depending on if the impact velocity is finite or infinite. In the second case, the Poincare map is well defined by continuation of the energy. The proof combines the study of phase-plane curves together with the “stretching-along-paths” notion.