Yes, though frequently the solutions are very similar to each other. For example, if you plot the future of an asteroid in 10,000 different simulations, you’ll

Yes, though frequently the solutions are very similar to each other. For example, if you plot the future of an asteroid in 10,000 different simulations, you’ll probably find that in most of them the asteroid remains in the asteroid belt where it started from, but perhaps in 10% of them it is perturbed enough by Jupiter that its orbit becomes a Trojan, or some other variety. If you look at the details of the 90% where it stays in the asteroid belt, you find that while they are all in different orbits from each other, the differences are not very significant. Just 9,000 rather similar orbits inside the asteroid belt. “Chaotic” usually means that the difference between two similar starting conditions grows without bound the longer you run the simulations forward. But orbits are closed loops; everything about an orbit is periodic. If two orbiting objects start near each other but have different orbital periods, then soon enough they will be far apart from each other. However, if you keep running time forward then they will end up right next to each other again. The distance between them is itself periodic, bounding the total error in a practical sense. Combine that with the overall stability of our solar system, and you find that most objects tend to stay in particular orbital families for quite some time. Most objects are near the bottoms of deep potential wells, and the forces that can push them out of those wells are quite small. It is only once they are pushed near the boundaries of those wells that rapid changes can begin to happen. Of course if it were any other way, then there would be nothing left in the asteroid belt by now. Compare that with Saturn’s rings, which simulations suggest will only last another 100k years, give or take a bit. They must be a relatively recent phenomena.