Some aspects of the non-smooth dynamics of an impacting inverted pendulum

In this work, we perform a systematic numerical investigation of the nonlinear dynamics of an inverted pendulum between lateral rebounding barriers. The attractor scenario is determined and illustrated by bifurcation diagrams. Attention is focused on local and global, classical and non-classical bifurcations that lead to the attractors-basins metamorphoses, and on the role played by invariant manifolds of appropriate saddles. Our numerical results show that the basins of attraction that appear at a certain critical threshold exhibit fractal nature. We also focus our attention on the onset of the scattered cross-well chaotic attractor.