Singularities in vibro-impact dynamics

The non-differentiable nature of vibro-impact dynamics can lead to breakdown of the global stable manifold theorem applicable to smooth dynamical systems. In one dimensional periodically excited system, the breakdown leads to the “shredding” of the stable manifolds, and this process is analyzed in detail. Bodily translation of filaments of stable manifolds can lead to homoclinic intersections, and this topic is discussed in the context of a new bifurcation due to “re-entrance”. Shredding leads to a strong similarity between the geometries of the singular subspaces and the geometries of homoclinic tangles and strange attracting sets.