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The relationship between symplectic properties and numerical accuracy is investigated using the dynamics of the Jovian planets as an example. What are the properties of symplectic integrators, including both their benefits and limitations, and how do they contrast with classical integration schemes? The dynamics of the Wisdom-Holman mapping appears to be different than that provided by very high order multipstep integrators. We will clarify the nature of such differences and how they affect orbital trajectories using elementary results in bifurcation theory. The significance of these differences regarding chaotic dynamics in the Solar system is discussed. Can the distortion of the dynamics by the Wisdom-Holman mapping lead to artificial separatrices and separatrix crossings---and to incorrect physical conclusions regarding the dynamics?
