COMPLETELY INTEGRABLE HOLONOMIC SYSTEMS OF FIRST-ORDER DIFFERENTIAL-EQUATIONS

We classify completely integrable holonomic systems of first-order dif ferential equations for one real-valued function by equivalence under the group of point transformations in the sense of Sophus Lie. In orde r to pursue the classification, we use the notion of one parameter Leg endrian 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.