This is paper no. 10 in the list on p. . Numerical methods for chaotic dynamical systems can often work, even when the classical theory says they shouldn't. Explaining why this is so, and coming up with a reliable means of telling when numerical results can be trusted and when they can't, is of extreme significance for engineering simulations of nonlinear systems. This is particularly important for the modern engineer who often uses pre-packaged software.
This paper, which culminates a series of papers on defect control for chaotic dynamical systems, answers the question completely, in the sense that it shows how to turn the question of reliability of the software into a question of reliability of the mathematical model, which of course has to be answered anyway.
This series of papers has been given favourable notice by members of the scientific computing community, and I have had several international invitations as a result.