  The symplectic Wisdom-Holman map revolutionized long-term integrations of
planetary systems. There is freedom in such methods of how to split the
Hamiltonian and which coordinate system to employ, and several options have
been proposed in the literature. These choices lead to different integration
errors, which we study analytically and numerically. The Wisdom-Holman method
in Jacobi coordinates and the method of Hernandez, H16, compare favorably and
avoid problems of some of the other maps, such as incorrect center-of-mass
position or truncation errors even in the one-planet case. We use H16 to
compute the evolution of Pluto's orbital elements over 500 million years in a
new calculation.
