I presented this in a meeting and got some good questions:
Are chaotic systems calculable?
yes, if you have extremely accuracy of the initial condition. There're two way to address this: 1. we continue to quest for higher precision. 2. we accept this difficulty and give up for precise prediction/computation
In addition, someone mentioned Kolmogorov–Arnold–Moser about the persistence of quasiperiodic motions under small perturbations, which can be seen as a special case when computation is desirable.