Gravity is strange stuff, and you don't even need General Relativity to see it do weird things. The book Fly Me to the Moon got me curious about low energy transfer orbits to the Moon that take advantage of "chaotic" behavior, and I'm now experimenting with Tony Dunn's freeware program Gravity Simulator 2.0, though I haven't gotten too far with it yet. I've created some simple models from scratch and played around with some of the scenarios supplied with the program and downloadable from his web site, especially some Earth-crossing asteroid cases (picture shows A2004 MN4, otherwise known as Apophis, one that will pass very close to us in the 2029-2036 time frame). It's pretty cool.
Using Gravity Simulator's ability to reference your view to any object, and to establish reference frames that rotate with particular objects, you can start to see "hidden" behaviors and patterns such as resonances with planets that can lead to surprising (chaotic?) changes in an asteroid's orbit (see Toutatis, for example - scroll down to the animated GIF - Cruithne is pretty weird too). User note: the scroll bar on the right controls the angle of your view of the orbits you create, and when you change the view or the scale, any object tracks that have been drawn are erased, which seems odd at first (you have to wait for them to re-draw, running time backwards if necessary to get back to an earlier point so you can redraw an interesting part of your path, like that asteroid buzzing the Earth).
I've found some web references with orbital data for low-energy Earth-Moon transfers, but so far I haven't been able to generate any of the odd looping orbits that are shown in this huge (4 MB PDF) "atlas" article covering some 280 families of these orbits. At least I'm getting a handle on it. GS is a much better tool than Orbiter for experiments like this that focus mainly on gravity and orbital mechanics and don't need the 3D views and other goodies that Orbiter provides.