This may be a bit pedantic, the nbody problem is not chaotic, it is harder, having riddled basins. > A riddled basin implies a kind of unpredictability, since

This may be a bit pedantic, the nbody problem is not chaotic, it is harder, having riddled basins. > A riddled basin implies a kind of unpredictability, since exact initial data are required in order to determine whether the state of a system lies in such a basin, and hence to determine the system’s qualitative behavior as time increases without bound. (Note this is different from “chaos,” where very precise initial data are required to determine finite-time behavior.) What is more, any computation that determines the long-term behavior of a system with riddled basins must use the complete exact initial data, which generally cannot be finitely expressed. Hence such computations are intuitively impossible, even if the data are somehow available. http://philsci-archive.pitt.edu/13175/1/parker2003.pdf http://philsci-archive.pitt.edu/13175/1/parker2003.pdf The above post is a good 'example' of sensitivity to initial conditions, and riddled basins do have a positive Lyapunov exponent which is often the only criteria in popular mathematics related to chaos. But while a positive Lyapunov exponent is required for a system to be chaotic, it is not sufficient to prove a system is chaotic. If you look at the topologically transitive requirement, where you work with the non-empty open sets U,V ⊂ X....riddled basins have no open sets...only closed sets. With riddled basins, no matter how small your ε, it will always contain the boundary set. If you have 3 exit basins you can run into the Wada property, which is also dependent on initial conditions but may have a zero or even negative Lyapunov exponent and is where 3 or more basins share the same boundary set...which is hard to visualize, non-chaotic, and nondeterministic. Add in strange non-chaotic attractors, which may be easier or harder than strange chaotic attractors, and the story gets more complicated. Sensitivity to initial conditions is simply not sufficient to show a system is chaotic in the formal meaning. But the 3 body problem's issues do directly relate to decidability and thus computability.