RK4

I seen a Schultz saying, about RK4, "it acts as a low pass filter". Considering we didn't have a detailed talk about a somehow difficult problem for a while (on this forum), it might be nice to reopen a debate about integrators. So a few questions. (If you have a hard numbers for behavior of other integrators, you might post them as well.)

Is problem with RK4 acting as a low pass filter, shared by a symplectic version of the algorithm?

Could you provide some on line accessible reference for misbehaviors of RK4?

What was your experience with bad behavior of the RK4?

Is there some problem that is extraordinally bad for RK4?

Edgeworth said it's bad idea to use for 3D problem a version of RK4 algorithm that wasn't designed for 3D space. How large would be a difference?

How many steps per orbit would you need for 2 body problem, if you'd like a stable orbit?

For 3 body?

How large would be a difference from a real solution? Let's say you'd use 2* of minimal amount of steps, and 50 steps per orbit.

This might be a somehow nice start. BTW I don't use RK4, I use a sympletic 6th order algorithm, that is braindead to implement, so I don't have experience with this type of integrator. (So don't expect I'd participate too actively in this thread.)