Research objectives and content
The first step is to understand the geometry and dynamics of untegrable hamiltowian systems near a singular leave of the lagrangean poliation. In other words, this concerns the generalization of action-angle coordinates as introduced by Lionville and Arnold.
Second objective is to adapt these results to quantum systems, using microlocal semi-classical analysis. This should lead to a generalization of the 1-Dimensional case treated by Y.Colin de VerdiUre & Bernard Parisse - this is the most innovative part.
Training content(objective,benefit and expected impact)
Being already embarked in a PHD in France, I am sure to find in Pr.Duitermaat in Utrecht an ideal complement to Colin de VerdiUre. I expect to benefit from Duistermaat's great knowledge to write an intersting dissertation. Furthermore, I expect to develop intellectual mobility, ability to talk about my results to a wider international audience and to stimulate the scientific cooperation between Utrecht and Grenoble.