Leafwise fixed points for C0-small hamiltonian flows

Abstract

Consider a closed coisotropic submanifold N of a symplectic manifold (M, ω) and a Hamiltonian diffeomorphism Φ on M. The main result of this article states that Φ has at least the cup-length of N many leafwise fixed points w.r.t. N, provided that it is the time-1-map of a global Hamiltonian flow whose restriction to N stays C0-close to the inclusion N → M. If (Φ,N) is suitably nondegenerate then the number of these points is bounded below by the sum of the Betti-numbers of N. The nondegeneracy condition is generically satisfied. This appears to be the first leafwise fixed point result in which neither Φ