The period of a pendulum can be accurately determined by an arithmetic-geometric map. The high efficiency of the map is due to superlinear convergence, which can be understood from a geometrical point of view by writing the map as a skew system (or master-slave system) whose master component has a globally asymptotically stable fixed point with order of convergence two, which reduces the behavior of the map to a one-dimensional dynamics. It is shown that the map shares many features with a general class of maps of the real plane.
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