Dynamical collapse of trajectories

Friction induces unexpected dynamical behaviour. In the paradigmatic pendulum and double-well systems with friction, modelled with differential inclusions, distinct trajectories can collapse onto a single point. Transversal homoclinic orbits display collapse and generate chaotic saddles with forward dynamics that is qualitatively different from the backward dynamics. The space of initial conditions converging to the chaotic saddle is fractal, but the set of points diverging from it is not: friction destroys the complexity of the forward dynamics by generating a unique horseshoe-like topology.