Completely integrable holonomic systems of first-order differential equations

Abstract

We classify completely integrable holonomic systems of first-order differential equations for one real-valued function by equivalence under the group of point transformations in the sense of Sophus Lie. In order to pursue the classification, we use the notion of one parameter Legendrian unfoldings which induces a special class of divergent diagrams of map germs which are called integral diagrams. Our normal forms are represented by integral diagrams.