Symplectic correctors improve energy conservation but not the accuracy of secular precession frequencies in 20 Myr Solar System integrations, because the {B,{A,B}} shadow-Hamiltonian term causes a non-oscillatory periastron drift.
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On the accuracy of symplectic integrators for secularly evolving planetary systems
Symplectic correctors improve energy conservation but not the accuracy of secular precession frequencies in 20 Myr Solar System integrations, because the {B,{A,B}} shadow-Hamiltonian term causes a non-oscillatory periastron drift.