UPDATE: I found another reference! While I always enjoy a good video starring Jimmy and Linda Carter, this one has Dennis Wingo describing ISEE-3's original Halo orbit. He describes Sun-Earth $L_1$ as "a point about 1.5 million miles from earth where a spacecraft can safely orbit without using any fuel."
The site http://spacecraftforall.com/a-new-orbit is an interactive thing - if you leave it alone it will usually start the video in about 10 or 15 seconds.
While finding some good patent examples to add to the question Spacecraft Maneuvers as Intellectual Property? Wow!, I ran across this patent:
US7744036B2 Method for designing an orbit of a spacecraft (J. Kawaguchi and K. Tarao, JAXA)
You can click on the PDF icon to download it.
My question comes from reading the following parts of these two sections:
BACKGROUND OF THE INVENTION
…By the way, it has been revealed by previous studies that if a Lissajous orbit is enlarged to a much more large scale one to enter into a non-colinear area, the non-linear effect makes the spacecraft trajectory closed. And the orbit of a spacecraft, if the spacecraft is positioned close to point L2 can avoid shadow by the earth and if the spacecraft is positioned close to point L1, can avoid passage in front of the Sun. When viewed from the Earth it looks like a halo around the sun, and thus is called a halo orbit….
SUMMARY OF THE INVENTION
As stated above, the natural halo orbit is adventageous on the fact that it is stable and draws a closed locus without any special artificial correction operation maintaining the motion. However, the natural halo orbit disadvantageously leads to an extraordinarily large orbit which must depart from a co-linear line connecting two celestial bodies. The distance may be as large as, for example, about one million km from the Lagrange point referred to here. The resulted natural Halo orbits around point L1 or L2 are too far and very much apart from the aimed points originally. Because of this, the merit associated with the halo orbits, that is, no maintenance of the position of a spacecraft is needed, is inevitably lost, if the trajectory is controlled and maintained artificially...
I take this to mean that when a halo orbit around an $L_1$ or $L_2$ point (let's say Sun-Earth) is sufficiently large, it is (at least within the CR3BP model) actually stable to small perturbations, i.e no station keeping is required for sufficiently large halo orbits about $L_1$ or $L_2$.
Question: Is this true? Are there other stable orbits associate with unstable Lagrange points?
I had always thought that all orbits around $L_1$ or $L_2$ were also similarly exponentially unstable just like the points themselves, (again, within the CR3BP model).
note: I am not asking a question about this patent. I am referencing it only because of the clear statement it makes about Halo orbits - this is where I read it. The patent discusses an artificially maintained smaller halo orbit. Halo orbits are a special class of Lissajous orbits where the in-plane and out-of-plane periods are equal so that it stays "open" and away from the central exclusion zone.
Figure 3 from the Patent US7744036B2: