I haven't looked for stuff from the last 20 years but I will ask around. I've got a book at home that you could figure out the bit about the Toda lattice if you read between the lines and I will look it up this evening.
A few extra points:
(1) People don't get academic credit for improving the exposition of things, only for making discoveries that are "new"
(2) You often see Poincare sections with anomalies such as tori that are folded over, the problem here is that the energy surface is not flat but has a topology like a sphere or toroid so you see strange things when you project these, I found in some cases you could make a three-dimensional visualization of the energy surface and draw the Poincare section on that and it would be more clear what was going on.
(3) The KAM theorem is stronger with N=2 oscillators (two q and two p coordinates) than it is with N>2 oscillators. With N=2 the tori are solid walls that constrain chaotic motion whereas with N>3 they don't have enough dimensions to really hold the trajectories inside so there are probably trajectories that go from one regular area to a chaotic area and then another regular area. One consequence of this is that we can't really say the solar system is table. Arnold talked about this in a hypothetical way a long time ago but this 'Arnold Diffusion' is still an undiscovered country.
(4) Despite that, people from NASA have done some very nice work at mapping chaotic trajectories that make it possible to get from one planet to another with much less energy that you would otherwise. See
you get these areas that look like television static that certainly have more structure than they appear. The proof that these areas are chaotic is based on the knowledge that, paradoxically, these are filled with stable periodic orbits and there is a fractal network of resonances that resonate with resonances and so forth that determines the motion in that area which is not visible because of the sensitivity to initial conditions and practical problems that come from doing the math. There were people talking in the 1980s that there ought to be a way to make better pictures with interval math but I don't think it's been done since then. Lately I've been interested in revisiting it not so much because I care about the science but because I'm always on the lookout for algorithms to draw interesting images.
