ROTATION NUMBERS OF HAMILTONIAN ISOTOPIES IN COMPLEX PROJECTIVE SPACES

In this paper, we prove the existence of symplectic invariants-we call them rotation numbers-for the time-1 map of a Hamiltonian isotopy in CPn-1. These invariants bear interesting properties related to the geo metry of the fixed-point set of the symplectic map. They are obtained by lifting the problem to the linear space C-n, and then using invaria nt generating functions to define them as solutions of a certain finit e-dimensional min-max method.