a third, fifth, seventh and eleventh order symplectic corrector for [[WHFast]{}]{}. Whether the high order-symplectic correctors provide any improvement over the low-order ones depends on the mass ratios in the system. For Jupiter-mass planets, a symplectic corrector of fifth order is no less accurate than a higher order one. If in doubt, there is no harm done in using a higher-order corrector as the speed implications are minimal. Thus, we implement the eleventh-order symplectic corrector by default.

Chaos Indicators
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A powerful tool for studying the long term evolution of Hamiltonian systems is the Lyapunov characteristic number (LCN). The inverse of the LCN is the Lyapunov timescale and gives an estimate of how fast two nearby particle trajectories diverge. If the system is chaotic, the divergence is exponential in time and the Lyapunov timescale is finite. Thus, measuring the LCN gives us an estimate of whether the system is chaotic and, if so, on what timescale.

A more recent approach with similar informative value is the Mean Exponential Growth factor of Nearby Orbits, or MEGNO for short [@Cincotta2003]. The MEGNO, $Y(t)$, is a scalar function of time, and provides a clear picture of resonant structures and of the locations of 