Hamiltonian flows on the space of star-shaped curves

We provide a geometric interpretation of the KdV equation as an evolution equation on the space of closed curves in the centroaffine plane. There is a natural symplectic structure on this space and the KdV-flow is generated by a Hamiltonian given by the total centroaffine curvature. In this way we obtain another example for a soliton equation coming naturally from a differential geometric problem 1]. Furthermore, we present a group action of the diffeomorphism group of the circle on the space of closed centroaffine curves.