Stachowiak (“stah-HOH-v’yak”) and Szumiński (“shoo-MEEN-skee”) 2015 builds on Morales–Ramis theory to prove the non-integrability of restricted versions of this system. A ratio of lengths denoted alpha must be a root of the formula “alpha-cubed plus six alpha-squared minus four lambda-squared plus four” for slow periodic energy exchanges to occur in a type of this system developed by Nikolaus Rott. An identical pair of these systems that feature “test” and “reaction” masses are used in (*) LIGO in order to filter out seismic noise. A central eye-shaped region in a fractal represents starting conditions for which this system takes especially long times to flip. For 10 points, name these pairs of harmonic (10[1])oscillators (10[1])commonly used (10[1])to illustrate chaotic (10[1])motion. ■END■