Unstable periodic orbits in the parametrically excited pendulum

We analyze chaotic motion in an experiment on a parametrically excited pendulum in terms of unstable periodic orbits. This provides a useful quantitative comparison with results of a faithful numerical simulation. Despite the presence of experimental artifacts, simulation and experiment are in good agreement. The analysis of scaling properties of both chaotic attractors along these lines remains, however, incomplete. Periodic-orbit analysis fails to account for their marginal hyperbolicity, and therefore fails to capture an important qualitative aspect of the chaotic dynamics in both experiment and simulation.