The following are closeups of dynamics near periodic orbits as seen in 16 Poincaré sections
equally spaced through a drive cycle of a parametrically driven damped pendulum. The circles
indicate a piercing of the Poincaré plane, and the points evolve as flip orbits, that is, they
alternate from one side to the other of both the stable and unstable manifolds. Also given are
the eigenvectors, eigenvalues, location of the periodic point, and the local coordinates of the
four iterates of the map.
