Are long-term N-body simulations reliable?

Abstract: Astrophysicists rely on solution for the N-body problem for a myriad of dynamics problems, from those in dark matter dynamics to those in planetary dynamics.  Over 50 years ago, Miller found that errors in our simulations of the N-body problem grow exponentially in time.  So why should one trust any such simulation over long times?  In this talk, I explore a three-body planetary system.  The motion over long times can be compared to recent results from Hadden & Lithwich (2018).  I find conventional integration methods are as accurate as more sophisticated symplectic methods.  In fact, a higher order symplectic method gave unreliable statistics in one test.