Dr. Goodings research interests are now in the area of nonlinear dynamics and chaos theory, particularly in the active field known as "quantum chaos". What is of central interest is to study the quantum analogs of classically chaotic systems. Using as an example a model of a billiard bouncing elastically in a wedge while subject to a constant downward force, he and graduate student Tom Szeredi showed how all the dynamical features of this classically chaotic system can be extracted from a knowledge of the quantum energy eigenvalues. They have also investigated the more difficult problem of going in the other direction, that is, of calculating approximate quantum energy eigenvalues from a knowledge of the (chaotic) classical dynamics. Current research is focussed on a scheme for incorporating the Heisenberg uncertainty principle into the classical-quantum correspondence.
In collaboration with people in cardiology at the McMaster Medical Centre, Dr. Goodings and graduate student Julie Lefebvre have used chaos theory to study normal heart rhythms. Their research has shown that there is an element of deterministic chaos in normal heart rhythms, although the evidence is not strong or persistent.