We examine the bifurcations of a piecewise smooth map that captures the universal properties of impact oscillators near grazing. In particular, we study periodic orbits with one impact per period and the way they are involved in the grazing bifurcations. We also show some phenomena that these orbits exhibit at grazing for some families of parameter values. © 1996 The American Physical Society.

• Received 5 September 1995

DOI:https://doi.org/10.1103/PhysRevE.53.134